Like many others, when I first learned of 5th Edition D&D and what Wizards of the Coast was attempting to achieve with it, I was fairly skeptical. Not only did their stated goals of bringing the fragmented D&D fanbase together and making the game modular sound overly optimistic, I honestly didn't think WotC had what it took to actually achieve such goals. And I say this as someone who didn't think 4th Edition was bad. I mean, it wasn't up to my taste, but for any 'roll-playing' (i.e. mechanically-focused) players, it was a pretty good game.
But in any case, I had doubts that 5th Edition would impress me. About the only thing I was sure of is that it would be newcomer friendly, since WotC has always put a lot of emphasis on making the game more friendly towards beginners and drawing in new players. That said, it was still a new edition of D&D, so I couldn't help but remain curious about it, especially after the few things I've read about 5e failed to give me a sense of the popular consensus. At one point last year, an acquaintance of mine said that they were organising a short 5e session and I finally opted to give it a try.
Now that I've used the system for several months and have played a good number of sessions, I can safely say that I've become a fan. It's a very fun and accessible system that still presents a decent level of challenge. Whereas 4th Edition was like an almost completely different direction for the series, 5th feels more like a logical evolution of 3.5 that actually addresses rather than sidesteps some of the fundamental issues that plagued 3.0/3.5. I would even go so far as to say that, at least to the extent that it was possible, 5th Edition was actually successful in achieving the goals WotC had set out for it. Maybe not universally, but for the most part.
It is true that the game is simplified compared to its predecessors, but it's surprisingly elegant in its simplicity. Most of the changes are quite sensible and serve to make the gameplay more balanced and intuitive. There are more viable options and fewer options that are essentially pitfalls, i.e. things that sound good on paper, but are underwhelming in practice, so it's easier to create a viable character. Furthermore, those characters are simpler to create and their progression is easier to keep track of. Admittedly, the system does either completely ignore or leaves vague some of the more minute aspects of the game for the sake of keeping things simple (like how there are no rules for sleeping or swimming in armour). That said, I personally haven't felt that this noticeably detracted from the game, since some of those aspects tend to be ignored or even forgotten by most groups.
This isn't to say the system lacks more significant flaws. The simplification didn't come without a cost of some customisation and there are still a few weak/redundant options, though customisation overall is arguably more meaningful. In addition, while definitely far more balanced compared to 3.5 and prior editions, it's definitely not as balanced as 4th was and casters once again have somewhat of an edge over melee classes. Lastly, the simplification has done nothing to make crafting less terrible; if anything, it's arguably worse (not that D&D has ever gotten this right, apparently -_-).
But in spite of its shortcomings, this edition is fantastic and the best I've played so far, which has convinced me to make it my tabletop RPG of choice. Combined with WotC's decision to reverse their backwards SRD/OGL policy, I see a bright future ahead for this game. If you're at all interested in giving it a try, I would highly recommend doing so.
On a side note, I've noticed someone mention Spoony's review of 5e. I'm a big fan of Spoony and his work; in fact, it was the Counter Monkey series that convinced me to try and stick with the hobby. That said, his review of 5e is easily one of the worst videos he's ever made. He himself admitted in the video that he did the review 24 hours after getting the book and without playing the game, and it shows. Not only did he make several factual errors, some of the arguments he made don't hold water when it comes to how the game is actually played. On top of that, significant parts of the video are essentially just vitriolic rants against what he perceives to be weaknesses in modern tabletop RPGs and their players.
I won't say that the review isn't worth watching, since it has its moments. But in terms of explaining how 5e is like, it's not exactly informative. So I would recommend supplementing it with other sources. In addition, if you have watched or will watch Spoony's review, you should consider checking out
Nerdarchy's response video as well.