Alright, here's my list of "4e things that made it into 5e."
Warlock as a default class.
Dragonborn and Tiefling as default Races.
*Arguable* - The "Eladrin" effect, where there is a more magical breed of Elf, and a more Forest-focused breed of Elf. (There have been tons of Elven subraces across a lot of D&D, of course, but 4e introducing the magical (or "high") elves as their own separate race with explicitly magical racial abilities really drew it into focus, a focus I feel is continued in 5e with their High Elves gaining a cantrip,)
The idea of "short rests" holding mechanical weight.
The mechanical acknowledgement of level consistent tiers of play, pre-Epic. (This ties to a LOT of stuff, such as Paragon paths, proficiency bonuses, 4e's ASIs being universal at levels 11 and 21, etc. etc)
I agree with that as far as I'm aware, the idea of the damage dice of your cantrips/at-will abilities scaling with your level is rooted in 4e.
Hit Dice being a partial reimplementation of Healing Surges
The removal of Arcane Spell Failure chance.
Technically, 4e "Trained" and 5e "Proficient" are closer to 2e's Non-Weapon Proficiencies, just adding bonuses to rolls instead of penalizing them to compensate for the privilege of getting to roll at all.
Fighter gets to keep Healing Surge, and partial retention of "action points" via Action Surge.
Monster stat blocks are a little closer to 4e in design, but they've changed with essentially every edition, so this can be viewed as more of a overall progression.
I would argue that the codification of Lair effects owes something to 4e's "Solo" monster designs.