Skills, races, armed combat, hit points, subclasses, monster design, a significant share in the classes. And the magic belongs to no one. 5e's just a lighter and less tactical system.
The 5e skill system is an only lightly modified version of the 4e one that gives up the half level scaling. First there are seventeen skills, plus languages- although 5e did add tool proficiencies. By contrast the 2e PHB has what? Over fifty "Non Weapon Proficiencies" in the PHB alone and more in extra books, most with their own subsystems? Plus thief skills? Then there's that there are basically three tiers of training in 5e. "Untrained", "Trained", and "Expertise". Which is basically the 4e approach of untrained, trained, and a little beyond that (e.g. Skill Focus); 5e is an only slightly lighter version of the 4e skill system. Further cementing it as almost pure 4e is the way that abilities modify it - for example the way the rogue gets to use minor, I mean swift, I mean bonus actions.
The races come next - and are very 4e in nature, starting with the obvious inclusion of Tieflings and Dragonborn in core. Two stats with bonuses and no stats with penalties for almost all races is again very 4e. As is the simplicity and cleanness of the racial abilities; dwarves for example do not get saving throw bonuses based on every 3.5 points of their constitution, bonuses to detect sliding/shifting walls, bonuses vs certain races, or racial class and level restrictions.
The armed combat rolls are the same as in 4e - Stat bonus (consistent) plus proficiency and level modifier vs AC. There's no issue round THAC0/Descending AC, classes having different attack bonus scaling, weapons getting bonus damage vs large creatures, or different weapons getting an inherently different ROF (other than the loading property). This really is the basic 4e engine - just without flanking or forced movement.
Hit points are barely rolled for in 5e; you instead get half your hit dice rounding up. And the healing model is closely related, with people recovering hit point thanks to long term endurance on a short rest and a lot of combat healing happening as a bonus. The difference here, of course, is that you started effectively at level 3 in 4e.
Subclasses are pretty much a 4e implementation; the game is built with them in mind (and they are in the PHB) and layer seamlessly over the basic classes with simple and clean bonuses and no stat minimums or special hinderances. Further pushing them into the realms of 4e is that an evoker in 5e, as in 4e, isn't a specialist wizard who gets more spells to cast from the evocation school but a wizard who is actively better at casting evocation spells in ways that aren't simple dice modifiers. 5e being a lighter version of 4e of course the powers get rolled into either base classes or subclasses.
The classes, for that matter, are all using 4e fluff. Paladins, for example, aren't going to fall and only one subclass is the morally pure (Oath of Devotion) - and no Pokemounts or normal mounts. Sorcerers have their random power sources (they were new to 3.0 and through 3.X were just "descended from dragons, I guess"). Warlocks, clearly are 4e (and were Monks even in 2e?). Rogues are sneak attack based rather than one off backstabs - and more importantly (and very 4e) are just better at some skills rather than having specific thief skills.
Monster statblocks are closest to a cut down version of 4e than anything else. The monsters have full stat blocks - but they aren't designed using PC rules the way 3.X is. Instead they have powers like Nimble Escape that let them do things. It's more a 4e lite approach than anything else, taking away the monster roles and using Legendary Actions and resistances for solos. Unfortunately there are 4e hit point levels without 4e tactics making them far more bullet sponges.
Even the magic system, which is its own thing but probably closer to 2e than any other edition (although completely dropped Vancian casting and is very different for different classes), has strong 4e influences from cantrips to rituals to spell focuses to sustain spells becoming concentration spells.
Edit: Backgrounds are a 4e thing as well - they were added to 4e
very shortly after launch. 5e slightly expands on them and gives them slightly more mechanical weight (full skill trainings plus a bonus). It's one of the very few places 5e has expanded on 4e - and the expansion is a good one.
Also I'm amused to see something
very 4e-theme-like being added to 5e in the form of the Dark Gifts/Supernatural Gifts, etc. The theme layer was, of course, added to 4e with Dark sun.
