I feel 5E is a descendent of 1E because that was my first role-playing game. It scratches much of the nostalgia. Then again there were many things about 1E I didn't like and I feel 5E generally does a better job at those.
Imo, it is a descendant of all of them- B/X and BECMI included. Or, more aptly, and evolution of them.
We felt like 3e was a better representation of how we ACTUALLY played the game, vs TSR's RAW version- with a bunch of extras thrown in. Like the unified D20 system.
This included, but isn't limited to, dropping odd, arbitrary "balancing" rules- like racial class/level limitations, in favor of giving humans their own advantages. ( YES! You can- and here is how!, rather than NO!!! because reasons) And dropping all the number crunchy wargamey stuff nobody I knew used. The general harshness of save or die's, or level/ability drains on the turn of a single roll, etc.
since then, it further evolved into 5th edition, adding new things, streamlining others.
A few things I love about 5E: cantrips as at will spells. Interesting focus options baked right in- ie subclasses. (if not always the implimentation of them, lol). What they did with Barbarians, Paladins, Wizards, and Clerics. Sorcerors are cool, too- I just am kinda meh with the general flavor options.
And you absolutely can play it the way we used to.
like any other edition, it isn't perfect, but it sure is fun to play! I just wish they'd included better DM tools for converting existing stuff to 5E- or adding your own. Determining CR, I'm looking at YOU. I think 3/3.5 was a sweet spot in that regard.