Like - Advantage/Disadvantage is #1 by a mile. It got rid of a big part of what I despised about 3e based games, the seemingly endless numbers of situational modifiers that had to be figured out as they changed each round. Worrying about what stacked with what...I'd rather have fun that deal with that mess.
Concentration - Helped git rid of the buffs which would be layered on until a foe cast a dispell and then lets take a few minutes to figure out what got removed and recalc all the mods. God I hated that.
The system doesn't assume that a PC of X level has X amount of gear. 3e PC was a pile of gear with a character attached to it that was almost useless at higher level without all that gear. 5e seems like a PC will have a lot less magic on them which is cool, your PC shouldn't be the gear, it should just help not take over.
Removal of emphasis on feats and tweaking your build and prestige classes, etc. Less options sure, but I'm fine with that as it seems to be putting the emphasis a bit more on the adventure rather than that next ding where you can fiddle with character abilities. Less time looking at the sheet for that feat to bust out and more time in the game with the other players as well.
Restoration of some of the feel and flavor of classic editions.
Not assuming you are using a grid and gutting of opportunity attacks.
Bounded accuracy. In 3e the numbers got out of control and unwieldy.
Dislike: Leveling is probably built more around fast leveling in an adventure path type campaign. Easy to fix though for a more long term episodic game.
Compared to 1e and BECMI I like the unified mechanics and streamlined rules.
Dislike: Rogues instead of thieves.
Overall its fun to play so far. 3e/3.5/PF are dreadful games on the tabletop past 5-6th level so I'm glad to have a modern D&D game I want to play and DM. It improves on the often disconnected nature of classic editions.
Note I never played 4e, had moved back to to a C&C/1e mashup game.