There are a LOT of reviews of 5th Edition up by now so I'll try to keep this concise. My Saturday night group tried out the Starter Set + Basic Rules (I'm not sure if the Basic rules are included in the Starter Set; I'm not the one who bought the box). Of the 4 of us, myself and the DM are the only "experienced" gamers, and that includes being the only ones who have played D&D before. We started this group because the DM's fiance and brother were messing around with FFG's Star Wars dice one night, asked him what the rolls meant, and were intrigued enough to want to actually play. So we played Age of Rebellion (with Edge of the Empire material) for several months, then moved onto short "campaigns" of Fate Accelerated, Fate Core, and now 5th Edition D&D.
This isn't the first time I've taught new players how to play D&D, but it's especially interesting teaching people who have played other games (especially more narrative games) a bit before vs teaching people who are completely new to roleplaying. As streamlined as 5th Edition is, there are some inherently unintuitive concepts ("what are these ability scores for when I always just used the modifier?") and the layout of the pregen sheet also posed some problems (skills, saves, and raw ability scores being in different places meant that a few times the players referenced the wrong number when a check was being made). That said, things went much more smoothly than they probably would have if we'd been using a grid and/or playing 3.x/PF, so 5th Edition is pretty newbie friendly compared with other editions of D&D.
The pregens we used were the Rogue (that was me), the Dex Fighter, and the Wizard. Arguably this is probably the most "hard mode" combination of pregens that we could have selected, but I think we've already bypassed the first big hurdle, which was that frightening first encounter. I'll try not to provide too many spoilers, but needless to say I think the only reason we survived was because the Fighter rolled a natural 20 on his Survival check to determine the direction that some horses had been shot from, and so the DM denied the archers the surprise round that they were supposed to get. The Wizard's Shield spell was a literal life saver, too. Of course also worth mentioning is that the DM has decided not to scale encounters back just so we can see how it'll play out, and the fact that we were able to survive (albeit barely) is a good sign.
The adventure itself seems to be pretty well-designed so far (I'm used to WotC published settings being pretty bad, and it's good to see that they've improved in this area). There are a TON of different hooks so that we all feel we've got a pretty full array of options to pursue even after just one session, and many of these are built into the backstories of the Pregens. This means that with a party of all 5 characters there would probably be too many different options and I can see choice paralysis being an issue, but that's better than being heavily railroaded.
Mechanically, the system is pretty slick. I'm a huge fan of Advantage/Disadvantage, and doubly so considering my Rogue doesn't have a reliable flanking buddy. The spell system was confusing for our newbie Wizard (especially since her last character was a very free-form spellcaster in Fate Core), but I think it's loads better than the Vancian casting of old. I'd even go so far as to say I might prefer it to 4E's power system, assuming option bloat from splatbooks don't become an issue. While the Rogue didn't wow me at first level, I'm looking forward to getting Cunning Action at 2nd and really ramping up the skirmisher shenanigans. It's worth mentioning that we couldn't figure out how Stealth and attacking from Hiding worked during the session, so the DM just ruled I'd get advantage for it (after looking up the rules later, which are in 3 different sections of the Basic PDF, which also happens to lack an index, I found out that we did it correctly). I'm still not super clear on how the Halfling's ability to hide behind larger creatures works. If the enemies see be run behind my buddy and then I succeed at my Hide check, I guess they can't see me so they'll take Disadvantage against me (and I'll get Advantage against them), but they'll know where I am. That seems very cheesy to me, and I'm not sure how often I'll make use of it because it stretches my suspension of disbelief a bit too far.
My favorite mechanic was Inspiration, which seems to work pretty similarly to Fate Points and Aspects. This made it really easy for our group to latch onto, and the DM was really good about generously throwing out Inspiration. The Personality/Ideals/Bonds/Flaws were written well enough to be very broadly applicable, probably even moreso than many of our Fate Aspects. The consensus was that it was easier to get Inspiration than it was to get Fate Points in play, though this is easily balanced out by the fact that in Fate you start out a session with 3 Fate Points. I suspect that many groups (especially those who have stuck with D&D and not branched out into systems like Fate) won't make as much use out of the Inspiration mechanics as we did. Because of the way it works it will come into play about as often as the group prefers it to, because the players and DM have to be active about asking for it and awarding it. For us, Inspiration had a huge effect on how the game plays, definitely disproportionate to the treatment it was given in the rules.
So at the end of the day the most important question is does 5th edition seem like a system that will be worth playing for my group(s)? Does it have enough of a niche to set it apart from all of the other systems that we play (or want to play)? The jury's still out on that one, but I will say that having the Basic PDF helps a LOT because it's always there for us to go back to and try out just a little bit more. I imagine that if we play again outside of the starter set I'd be tempted to pick up the PHB, but only time will tell. The way I'm looking at it now though, the biggest selling point for me is probably the grittiness of the system. My go-to fantasy RPG is 13th Age, but it's really tough to make that game gritty because it's all about the PCs as Big Damn Heroes. Sometimes I get the itch to run (or play) something that's a little more Sword and Sorcery, and I think 5th Edition could be that game. I've heard a lot of people comment that there are already many retro-clones that emulate such an experience, and if that works for some people, that's great! But 5th Edition also brings to the table the superb Inspiration mechanic, as well as Advantage/Disadvantage, and perhaps other neat little bits that I haven't come across yet after just one session of play. And then there's class design in general, which is different enough in 5th Edition to be worth looking at. I'm not sure whether 5th Edition does most classes better at this point, but the way that spells work for the Wizard is really nifty, and the Rogue seems like it will play somewhat like a 13th Age Rogue in some aspects after a few levels, which is a HUGE plus in its favor. I don't have strong opinions on the Fighter yet, and haven't seen the Cleric (or obviously any PHB classes) in action. Overall, color me intrigued. A gritty, fast-paced (oh yeah, I did mean to comment on how quick the game runs) game with a smattering of "modern" and more narrative mechanics might have a bigger potential niche than I expected this edition to have. Based on many reviews I've read the game is largely perceived to be "more of the same," which in some ways might be true but there are enough little changes that it's not quite that simple in my opinion.