The thing I think D&D 5E got right is that it maintains the feel of D&D (in all its forms) in my opinion. And this is both from the mechanics, but more especially the narrative and story and fluff and art.
Having a game with all the normal species presented as they are in presentation, story, artwork and slight mechanical heft feels like D&D to me. Having the story and fluff of all the classes feels like what Dungeons & Dragons has been and always will be. Even when another game has similar classes, they are not presented in such a way as to evoke what I think of as 'Dungeons & Dragons'. Using the d20 as well as all the other polyhedrons in the way they are feels very much like what I expect D&D to feel like. Having ability scores go from 3-18 (or really 3-20) even though THOSE numbers don't even have an actual effect (and its the modifiers that do instead) evoke Dungeons & Dragons to me. Terms like 'Armor Class', 'Saving Throw', 'Ability Scores', 'Spells', 'Adventuring Gear', 'Hit Points' and so on and so forth all evoke my interpretation of what D&D is.
It is all of these things combined (with some new ideas occasionally showing up and other ideas going away depending on the edition) that make something feel like D&D done right. Even the more maligned editions according to various people (whether that be 3E, 4E, 5E, or even AD&D, 2E, or Basic D&D to some) all still have a huge number of these signposts and signifiers that scream Dungeons & Dragons to me, so I have not once had an experience where a D&D game I read and played didn't feel like it. Heck, to the surprise of no one, even Pathfinder feels like D&D to me.
Which is why if someone asks me if I want to play 'D&D', I'll say 'Sure!' And it does not matter in the slightest which edition you pull out and put on the table. For while the mechanical systems of the various editions might go in slightly different ways... the feel of the game will always be the same. It's all D&D to me, regardless of what edition we are playing.