So where did D&D 5E succeed? From my experience in DMing it to my local group, its great success lies not necessarily in its particular rules, but rather in the fact that it managed to distill the very essence of "Dungeons and Dragons" into one edition. It is neither a homage to the "new school" world of system mastery and tactical combat, not a carbon-copy of old-school with all its many subsystems; but it gives me the feel of running "D&D", the feeling I first felt when I first made my very faltering steps to DMing AD&D 2E to a friend and his brother back in 1997. It seems as if the designers, instead of trying to innovate in terms of game mechanics like they did in 3.xE and in 4E, tried to figure out what "D&D" is, in its most basic core, and build a game around that.
It feels like D&D. It plays like D&D. It runs like D&D. The game would be familiar to anyone who played any edition, especially B/X, 2E and 3.xE. Some mechanics, such as a unified task-resolution system, come from 3.xE, some, like the healing mechanics, are closer to 4E, but the very core feels older, even timeless. All the tropes are back, multiclassing and character optimization are pushed back, but not erased totally. I'd say that almost any person who liked any edition of D&D would love 5E, with the possible exception of those who enjoy focusing on the 4E tactical-combat system, which was greatly dialed back in 5E.
In short, highly recommended.