That was once known as "D&D Next" has been released as Fifth Edition Dungeons & Dragons. Sorta. Mostly. We don't quite have the Monster Manual (Well. This has released since I started drafting this post) or the Dungeon Masters Guide yet but we have the Players Handbook, a Starter Set that has a streamlined rulebook and an introductory adventure, the first half of an Adventure Path (Hoard of the Dragon Queen), and free PDF "Basic Rules" files that let you build a small set of characters out to level 20. And there's been some restructuring to the organization so you don't really need the DMG to run a campaign. The DMG is supposed to be mainly a repository of optional rules "modules" and hacks to modify the game. I believe magic items are back in the DMG now, but if you run the Starter Set or Hoard of the Dragon Queen they list some magic items there, and there is an online supplement for the latter that lists the magic items you need there.
In fact this whole digital thing is an interesting departure for Wizards of the Coast. Although you'd only have a few class & race choices for PC's it's entirely possible to buy Hoard of the Dragon Queen, download the free Basic Rules and the online supplement and you have everything you need to run a campaign up through level 7. When they release the second book in the Tyranny of Dragons Adventure Path they plan on updating these files to cover that and you've got an entire campaign and you're only out $60 (retail cost, less if you shop Amazon or get a deal). And the rules are all compatible, so you can have one player using the PHB and really tweaking out his custom fighter while his party-mates just run the stock cleric and wizard from the Basic Rules.
This is a big departure from fourth edition where A ) WotC was releasing a new hardcover book every month and B ) the only online concession was the generally terrible software provided as "D&D Insider". Of course, time will tell what happens next year to the game, and there was a lot of talk a while back about how Hasbro was insisting D&D needed to achieve Magic-level sales or they would just shelve the brand. I saw an interview with Mike Mearls (lead designer of 5th edition) where he explained that the plan now was that a healthy D&D leads to video games, media tie-ins (books, movies, cartoons), and even toys and the like. He made a major point of saying once you have the core three books and the Adventure Path you have years of gaming and does putting out more rules enhance the game? Maybe it doesn't.
So all this babble is great background, but what do I think of fifth edition so far? I like it a lot. I've run two sessions from the Starter Set adventure, read through the Players Handbook and I'm reading Hoard of the Dragon Queen currently. My one sentence summary of the differences is this: Recent RPG's had become complex system of rules focused on letting GM's and players tell each other "No", whereas fifth focuses back on telling GM's and players to work together to tell entertaining stories. When I play many games the experience is this back and forth where rules and rules exceptions are stacked up and compared until an answer comes out. When a player asks "Can I jump over the bar and then run up to this bully and knock him over?" everybody wants the answer to be "Yes. Or at least you may certainly try". We don't have to first look up the rules for the DC of a bar jump, then figure out how much movement that should take up, then check to see if the character has any feats, class features, or magic items that modify the attack roll, then figure out what the bully's defense is (which can be impacted by feats, class features, or magic items) and then finally make the roll. Oh but wait, the bully hasn't gone yet so he's flat-footed which means all his defenses are different, and does this magic item work when the owner is flat-footed? You want rules that give you some quick and dirty ways for a GM to make a quick judgement call and move on.
I never used a battle mat with first or second edition D&D, or even GURPS. I skipped third edition when it came out, so fourth was my first exposure to a system that really requires a battle mat. In theory it should make things easier to see and allow for cool terrain effects and so on. In practice getting terrain effects perfectly balanced against player powers so they are neither over or under-powered is difficult and the battle grid ends up providing more "No's". "Well you can only move 30 feet and that guy is 35 feet away." "Those squares are difficult terrain so they cost more, and that's your second diagonal square so it costs double". "Oh but is the difficult terrain due to forest underbrush? At level 3 I took Forest Stride so I can ignore that difficult terrain" Uggh. Ask "Can I hit the guy?", get an answer and move on.
There have been a lot of posts around the web about what fifth brings to the table, so if you're interested you really already know. I love replacing a whole host of little modifiers with the concept of advantage or disadvantage. (Rogue protip: advantage gets you Sneak Attack. If your DM has given you an inspiration point for playing to your flaw or bond then you can spend that inspiration on any attack, which means you get the normal advantage AND Sneak Attack. We realized that in the last session I ran and it's super-powerful.) It makes things move so much faster at the table. I think the "spell slots" do a good job of balancing old-school Vancian magic with a bit more flexibility than wizards and clerics usually have in fantasy games. It also solves a weird problem where Magic Missile is always an awesome spell and at high level you don't have any other use for first level spell slots: you can cast Magic Missile as a fifth level spell or as a first level spell and the spell scales accordingly. I love the stripping out all of the crazy math treadmills where everyone gets a +1 to their attacks and then all of the monsters get a +1 to AC for a net no change and you reach these silly values attack rolls where you're rolling a d20 and adding 27 to that value.