Before I get into talking about the game of Dungeons & Dragons, 5th Edition, I want to talk about something that I believe is conceptually distinct from the game--especially since, unlike essentially every other tabletop RPG publisher, 5e is owned and marketed by a big corporation, Hasbro. Nevertheless, it needs to be said that D&D 5e is pretty expensive, and probably more expensive than it should be. The three core rulebooks for 5e have a MSRP of $49.95 each, for a grand total of $149.85. For that $49.95, you get between 316 (Players Handbook) and 352 (Monster Manual) pages of content. By contrast, the Pathfinder Core Rulebook is also $49.95 MSRP, is 576 pages, and includes the rules material of the Dungeon Masters Guide. The 13th Age Core book is $44.95, 319 pages, and doesn't require any other books (though, you really should get the 13th Age Bestiary, which is a top flight monster book). And it is not like the production values of D&D are orders of magnitude better than their competitors--all three are full color, hardcover books, and I think it is defensible to say that both Pathfinder and 13th Age are nicer visually than the 5e books. It's also defensible to hold up 5e above the other two visually, but I don't think you can say that you are getting some categorically superior product from 5e.
Yes, I know you can get 5e books much cheaper on Amazon--a little over $85 for the set based on a recent Amazon look--but keep in mind that this kind of online discount model is a killer to local game stores, and so is uncool in its own way. But even with these steep discounts, you still end up with a total initial cost-to-content ratio that is similar to Pathfinder. And that's just considering the print books; if you factor in the digital dimension, 5e is flat-out non-competitive. The Pathfinder Core Rulebook and Bestiary are $10 each for the PDF; the PDF of the 13th Age Corebook is free if you buy the print version on Pelgrane's website or submit your proof-of-purchase from a game store. By contrast, if you want digital versions of the D&D books, you must first get a subscription to a separate service, D&D Beyond, which allows you to purchase the books for $29.99 each. Oh, and you can't read the books offline, as all you are really buying is the right to access the file on D&D Beyond's servers, not the actual file itself. Again, I know a portion of the necessary content is available for free, but so is the overwhelming majority of the necessary content for Pathfinder and 13th Age, far more than what is in the 5e SRD. There are many reasons to like and favor 5e over other competitors, but I think it is worth saying that buying into 5e is going to be more expensive, no matter how you cut it, then getting into other games.
OK, let's talk about the game. But, in a sense, that's the problem--you can't really talk about 5e as a game without talking about the broader context of Dungeons & Dragons as a whole. The tabletop RPG hobby begins with the original "white box" D&D in 1974, so in an important way this entire space is defined by the game. Since '74, there have been only two periods of time when D&D was not the dominant game in the hobby, both in terms of sales and in terms of community engagement--the late 90s at the height of Vampire: the Masquerade (when, by the way, the original publisher of D&D was in the process of avoiding bankruptcy/being sold to Wizards of the Coast) and from about 2011-2014 when Pathfinder was outselling 4e (Pathfinder, of course, being a D&D derivative, so in a sense that doesn't even really count). D&D has an enormous legacy and (though I hate this word) "brand identity" that is unmatched by any other tabletop RPG.
Based on interviews I have seen, the designers of 5e understand this in a way that I don't think their predecessors did. The challenge of designing 5e was not simply about designing a game, but about positioning their game in this broader context. And the challenge was greater because large slices of the broader D&D community really didn't like the last official offering, 4e. The extent to which that sentiment was fair or unfair is basically beside the point--they had a group of disaffected customers who they needed to convince to come back into the fold.
Moreover, while D&D is a powerful brand that does have core characteristics, the game has gone through a series of expressions, expressions that are often radically different from one another. To take just three examples out of many you could pick, you have the rules light, somewhat free-form gritty dungeon crawl expression that marked the earliest versions of D&D and has coalesced around the moniker of "the OSR"; you have the more tactical, high adventure style that came to the forefront around the time of 3rd edition (and, I think, during the peak popularity of MMOs like World of Warcraft); and you have the more story-focused version with complex plots and extensive character development, now highlighted on many streaming games. Each of these styles emphasizes different parts of the broader D&D brand, leading to conflicting priorities from a design perspective.
When the project that would become 5e was announced, it was clear that a core design goal was to try to bring together all of the folks playing all of these different versions and expressions of D&D under one roof. This is an insanely difficult design goal, and in a maximalist form is actually impossible. D&D is too broad a thing, and the preferences of the OSR crowd vs. the Pathfinder crowd vs. the Critical Role-inspired crowd are too divergent, to create something that is all things to all people. Much of the talk on the internet in the early stages of the playtest was that this project was going to be a disaster, and I don't think that was pure haterade or trolling. Something that tries to be all things to all people often ends up being not much to very few.
Instead, what we got was a version of D&D which is most things to many people. That might sound like damning with faint praise, but I don't mean it that way; I think 5e is the absolute best it could be given the extremely difficult and divergent set of masters that it has to serve. It had to "feel" like pre-3rd edition versions of D&D and have space for the "rulings not rules" style of game management, but it also had to provide character design complexity and options for the post-3e fans. It had to give space to people who wanted to engage in more free-form role play and character work, without scaring off the people who are suspicious of (or even hostile to) more narrative or story-oriented games. And it basically does these things.
Part of the way it manages these conflicting agendas is to avoid killing any sacred cows, but still subtly nudging them in certain directions. Take for example the spell system. Every edition of D&D except 4e uses a spell slot system, where a caster gets a discrete set of slots which can be filled by particular levels of spells. That is an iconic feature of D&D, and there was a significant segment of the fanbase that would insist on that system being present. And, so, 5e has a spell slot system that works more or less like it worked in previous editions. But it is not exactly like previous editions. Spell slots can be used in a much more flexible manner than in previous editions, and there is an easy-to-implement optional rule that converts them into an undifferentiated pool of spell points (long a bugaboo for a certain sort of D&D fan). In addition, 5e beefs up at-will cantrips to add effective damage dealers, eliminating the problem of (especially low level) spellcasters running out of spells and being forced to resort to firing crossbows or whatever--which was a key problem 4e was trying to solve.
If you were starting from a blank sheet of paper, you could probably come up with a simpler and cleaner system (there are at least one too many different paradigms for knowing/preparing your spells, and as much as I like them, it feels like the Warlock's mechanics are from a different game). But the 5e designers were not starting from a blank sheet of paper--they had to have a system that was recognizable to people who are really committed to keeping the spell system "feeling like D&D," while making some significant improvements on what came before. And that's basically what they did with the spell system, and it is repeated throughout 5e--small, conservative, but noticeable "nudges" to update and streamline the basic D&D experience.
Another example can be found in the class design. Old school D&D has very simple and predictable classes--every OD&D fighter is mechanically the same and gains the same abilities at every level. The design trend from that point was toward greater and greater character customization, culminating in 3e/Pathfinder (and 4e as well), with its emphasis on the character building mini-game and finding synergies between different feats and so on. This was perceived, rightly in my view, as overly complex and too punishing for new players, as the gap between optimized and non-optimized characters was quite high. 5e has a very predictable and streamlined class structure, in the sense that most of the time there is a set power that a character gains up going up a level, removing the need to consult long lists of potential choices and look for powerful combinations. Instead, each class allows the player to pick a single option from among a list of subclasses for their class. So, there are customization options, but those options are in big chunks as opposed to discrete, smaller options. Likewise feats are recast as bigger "plug-in" abilities as opposed to smaller abilities (or, as in 13th Age, upgrades to otherwise existing powers and spells) and are made technically optional. It's more complicated than the OSR people usually favor and has fewer options than character build devotees would favor, but there is a little bit for both of them.
That's not to say everyone loves 5e or that everything lands. One of the players in my online gaming group, who has experience with previous editions of D&D, basically thinks 5e is the worst of all possible worlds--too many fiddly bits and old school hold-overs to be a strong narrative system, but too stripped down mechanically to be interesting for tactical combat (he was shocked when I told him how successful 5e has been). And while I don't totally agree with that, I see where he is coming from, because I think 5e is intentionally trying to exist between a set of poles. Despite the fact I basically like 5e, there are definitely things in the game that feel like poor substitutes for other, more robust solutions found in other games. For example, the whole system of backgrounds and the Inspiration die feels completely tacked-on and half-assed, trying to give some support to out-of-combat activities and character development without actually doing so. Plus, I hate systems in which the DM/GM is supposed to judge and reward in game mechanical terms players for "good role playing," whatever that means--the GM has enough on his or her plate, it feels arbitrary, and I don't find it actually encourages character investment where there otherwise would be any.
Having said that, I do think that 5e meaningfully pushes D&D in the direction of a more narrative, story-focused experience. Mike Shea (a/k/a SlyFlourish on social media) has a recent article along those lines, and I think he is right that by reducing the complexity of the game, especially with regard to combat, you end up de-emphasizing the tactical orientation of the game. I am of the view that 5e didn't create this trend (I think it has to do with a broader realization that a narrative-focused game is what tabletop RPGs are best at, especially as compared to video games), but there is no question that 5e is positioned to drift in the broader current in a way that some of its predecessors were not.
This dovetails with the fact that some significant measure of 5e's success is a result of it being the game that Critical Role plays. This of course raises the great "what if"--prior to streaming when it was a home game, the CR crew was playing Pathfinder, and switched over to 5e when it went on the air. What would have happened if Mercer et al. had stuck with Pathfinder, even if in a hacked form? (I bet the Paizo folks have wondered about this). The problem with this hypo is that it points to the same problem with Pathfinder that caused Mercer to switch in the first place--Pathfinder is just too much for most folks, especially people coming into tabletop RPGs. If people who loved Critical Role have to digest the dense 576 pages of the Pathfinder Core Rulebook as an initial entry point for translating their viewing experience into a game, it is likely that they would be scared off. Especially if Mercer was telling them "yeah, we are playing Pathfinder, but we are hacking it and not using many of these rules."
Finally, even putting aside Critical Role specifically, 5e has benefited from the rise of streaming. The conventional wisdom right now is that rules-light is the way to go for streaming, and 5e's stripped down nature fits into that mold quite well. The decision to default to using a grid, but without the complex movement and flanking rules, seems perfectly suited to streaming, since it provides a visual hook for viewers without getting bogged down. Mike Mearls and the other 5e designers have been candid that much of this is a happy accident as opposed to a conscious choice, but nevertheless there are clear advantages to 5e from the standpoint of streamers and streaming. And the Wizards of the Coast folks, smartly, have leveraged their resources and brand capital to promote streams and streamers. Their D&D Twitch channel has, at least as of the recent version, nine different campaigns going on throughout the week (plus simulcasting, or at least promoting, Critical Role), and they have put on streaming-focused events to promote their projects. Last year at Origins they had a streaming booth set up in the main D&D room. They have clearly embraced the idea that streaming brings people to the game that wouldn't otherwise check it out, and more specifically brings people to their game, and it is hard to argue that they are wrong about that. They have been handed a gift with the rise of people liking watching other people play D&D, and they are running with it.
Much of this rising tide, again, has to do with the "brand power" of D&D. No one who does not play tabletop RPGs has heard of Pathfinder or Call of Cthulhu or 7th Sea, but pretty much everyone has heard of Dungeons & Dragons. To the extent that the concept of tabletop RPGs as a whole becomes more popular, that popularity is going to disproportionately benefit D&D. All 5e has to do is be positioned to capture the fruits of the broader popularity, and 5e has done that very effectively.
The bottom line with 5e is that for any single thing you might want to do with it that is within the broadest possible definition of D&D, you can probably find a similar game that does that thing better. But, if you want a single game that supports many different play styles, or you want to serve players that want different or incompatible things, or you don't know what you want because you have never played anything like this before, 5e provides a really compelling product to serve those different ends. I said in the 13th Age review that it was an opinionated game; 5e, by contrast, is very intentionally not opinionated, and that is the best thing about the game. 5e is like modelling clay, in that you can do most anything with it. There is a real virtue in that, particularly as that was what they were going for in the design of the game. 5e is a game that hits its target, so long as you are clear about what the target is.