I’m collecting recommendations here for my kid, who is nearly 11.
He’s a big fan of Gravity Falls and Star vs. The Forces of Evil, both Disney shows (albeit not standard Disney fare).
I’ve head lots of good things about Steven Universe, though I’ve never seen any episodes.
Any other good, recent animated shows out there? Let me know!
[And no, Rick and Morty isn’t a kids show. :D]
Adventure Time
Aww why does it have to be within the past five years? Honestly I haven’t cared for hardly any of the kids shows this century just because of the preference for, imo, shitty art. I mean, what about the classics like Animaniacs? Gargoyles? The Tick!!! Hell, the only kids series I’ve really enjoyed in the past five years has been Avatar TLAB and Korra. Oh and…maybe…Gumball… . But check out this list. It’s got a lot of good shows on it.
Adventure Time, Steven Universe, Clarence, Star Wars Rebels, Over the Garden Wall (a miniseries, but it’s worth seeking out)
I think he’d definitely be into Over the Garden Wall.
Star Wars Rebels he disliked the animation style (maybe too “uncanny valley” for him).
He likes Adventure Time. I’ve not heard of Clarence.
Bob’s Burgers has won a few Teen Choice Awards, so even though it’s a primetime sitcom I think kids would like it. And it’s appropriate for kids. The kids make up more than half of the show!
I do agree with **AngelSoft **- “recent classic” cartoons do still hold up. Animaniacs, The Tick, Tiny Toons, the original TMNT, Ghostbusters, Scooby Doo, Duck Tales, Talespin, Darkwing Duck and Home Movies (by the same guy who does Bob’s Burgers) come to mind as ones that I enjoyed and can definitely see kids today enjoying as well.
Seconding pretty much all the suggestions. I enjoyed Uncle Grandpa because I like irreverant and literal humor and that show is chock full of it.
If you’re not worried too terribly much about violence you could spring for some anime? Naruto, DBZ and One Piece are action packed without being TOO terribly adult.
One Piece? Do you want to kill them?? There’s nearly a thousand episodes! It’s the devil’s show!
**Avatar: The Last Airbender **is a favorite of my kids.
Also Samurai Jack, Dexter’s Lab, The PowerPuff Girls.
My kids are 5-7 years older, so those were the cartoons from just prior to your criteria of “last 5 years.”
My son is 2, so I’m putting in his favorites here for anybody who also needs something for a toddler: Sarah and Duck is a British show that’s pretty delightful, even for us, which is good because otherwise we’d burn the house down; Trotro is a French one that we’re about to light the matches with (nothing wrong with it, it’s just really FOR TODDLERS, where as some of the others can be enjoyed by anybody), Octonauts is super cute and really for kids a little older, Puffin Rock is Irish, beautifully animated, and also very sweet. I’d say everything but Trotro can be enjoyed by kids quite a bit older. And before we’d seen every singly damned episode of Sarah and Duck ten times we used to keep watching that one when Farticus went to bed.
I love me some Phineas and Ferb! Fun stories and catchy songs, what’s not to love?
The Amazing World of Gumball
I second the votes for Gravity Falls and Amazing World of Gumball, both great shows.
Wander! Wander! Over! Over! Yonder! Yonder! Wander! Yonder!
Dit dit dit dit dee dee, Wander Over Yonder!
SpongeBob, Courage, Billy & Mandy…
This.
Not typical animation, and one of the show’s main characters is a talking goldfish…with legs…named Darwin. Delightfully subversive.
Heh, see, this is why I created the thread: I’ve never even heard of this show. 
Avatar: The Legend of Korra
Star Wars: the Clone Wars
Star Wars: Rebels
Phineas and Ferb is awesome.
Fullmetal Alchemist: Brotherhood.
Okay, it’s six years old, but come on.