Humans are the least changed - but like everyone in DS they have psionics as a baseline.
All the other races are more changed. I think in most cases they'd be fine as a subrace:
Dwarfs - Taller and heavier than AD&D Dwarves, are way more obsessed with their tasks, too getting a mechanic called "focus" - in 5E this might give Proficiency or Advantage on certain rolls. This is a huge deal - they can change their focus (but it has to be a task that is likely to take at least 1 week), but if they die with the task unfinished, they become banshees! DS art typically depicts them as beardless.
Elves - extremely tall and skinny (6'6" to 7'6"), incredible endurance runners, nomadic non-civilized culture. Resistant to heat and cold.
Half-Elves - Athasian Half-Elves are particularly outcast and self-reliant, rather being being big friends with everyone. They learn survival and get an animal companion. Probably change to +2 WIS instead of +2 CHA.
Half-Giant - 10-12ft tall (so no pretending they're not size L), 1600lb massive, well half-giants (the 4E deal where they were Goliaths was just stupid, and I say that liking both 4E and Goliaths, note). Always Lawful in alignment in 2E, but I suspect that could change to a mechanic of some kind in 5E. It's hard to say exactly how their other racial traits could work in 5E without being OP - in 2E they got +4 STR +2 CON and -2 to INT/WIS/CHA, and they doubled their HD rolls (before CON mod). I think really they should develop a 5E equivalent of 3E's "level adjustment" for them, and as everyone else starts at 3rd, them starting at third but getting effectively otherwise being L1 (and thus staying 2 levels behind) could work pretty well. I suspect just maxing their HD rolls would be fine - it's not much more than the Toughness Feat, which is legendarily
Weirdly they weren't much of a problem in 2E, and people weren't even that keen on playing them.
Halflings - Terrifying little cannibals with a kind of Darmok and Jalad thing going on. Ability-wise they're basically Halflings so could definitely be a subrace.
Humans - more exciting colours than usual (including ones not regarded as human), and then tend to be mutated in minor ways (as befits a post-apocalypse).
Mul - Half-Dwarf, Half-Human, all endurance. 6'+, completely hairless, ripped, and capable of working for literally days on end without any kind of rest (beyond eating/drinking). Sterile. Bred as slaves. Had +2 STR, +1 CON in 2E, probably would in 5E too. They'd probably ignore the first two levels of Exhaustion they acquired in 5E (at least), and that would refresh on a long rest.
Thri-Kreen - Massive (size L again, but I suspect M versions would be okay, I guess, and I'm pretty sure they used size M weapons, because their limbs aren't that big) Praying Mantises who can talk and think and so on (not humanoid at all). 4 limbs (doesn't give extra attacks, though they can bite as well - probably make that a bonus action in 5E), significant natural armour (AC5 in 2E, probably AC13 or 14 in 5E, because natural ACs tend to be lower), bite and claw attacks (only 1d4 damage though), massive leap (20' up or 50' fowards), know how to throw crystal chakrams, can dodge missiles due to fast reflexes. Also at 5th they could paralyze-poison people with their bite (would be a Feat in 5E). +2 DEX +1 WIS, prob. would stay the same in 5E.
Aarakocra are also buzzing around, and could be used largely unaltered (save for adding Psionics). Pterrans we're not going to talk about because they're just dumb rubbish lizardmen and their addition to the setting as a playable race is one of the most inexplicable things that happened in the second 2E boxed set (which was complete drivel compared to the first - I blame the Prism Pentad, some of the worst D&D fantasy novels, which is saying something!
As for later races, Genasi and Dragonborn (Dray) are a natural fit, but Tieflings (sorry guys...) and others... no.
