Off-topic, but though it's not 5E, check out Pillars of Eternity (released in March). It's pretty much exactly what you are looking for.
Played it. Three times. It's good, but it's not really Epic-scale (3 complete run-throughs... all quests... took me 75 hours, which is what I've spent on a single play-through of Baldur's Gate 2) and the NPCs are fairly bland (excepting a certain midwife and a crazed cleric...). Good story and gameplay, though.
It's kind of hilarious how much it rips off D&D. Same classes, most with the same abilities. Sort of a merge between 3e and 4e. I was rolling my eyes hard as I went through the spell lists for my wizard. 1st level: burning hands, magic missile, shield, etc - with different names. 2nd level: scorching ray, mirror image, etc - with different names. 3rd level - fireball, lightning bolt...
The thing about D&D, though, is that it's more than just the rules. It's also the setting and the monsters and the *feel* of it. Regardless of my ambivalent feelings on the Realms, it's kind of nice to see Waterdeep show up. Or Neverwinter. Or... gods save me... Drizzt, or Elminster, or Mordenkainen, or Vecna, or Tanis Half-Elven, or Kylie the Tiefling Tout.
Pillars of Eternity may basically be the D&D rule-set, and a very good game in it's own right, but it doesn't have mind flayers. It doesn't have the Great Ring of Planes. It doesn't have the Blood War. It doesn't have the immense lore and background that D&D brings to the table. It doesn't directly attract new players to the tabletop game. I'm less excited to hear about the politics of the Dyrwood, when I could be hearing about the latest news from Solamnia, or Cormyr, or Sigil, or Barovia.
...which, now that I think about it, ties back into my original point about what I love so much about the game. The rules really don't matter, as long as they're not actively getting in your way (like 3e / Pathfinder used to do for me, as a DM). It's all about the story, the setting, the shared experience. So, much as I enjoyed Pillars of Eternity, it's still not taking the place of the continuing stories of Minsc and Boo... Xanathar the Beholder... the never-ending troubles of Neverwinter... or what happened to the Nameless One after he found out who he is/was....