What are some fully controller supported games that are good for a 5 year old?

Some of LEGO series might be good, they are a lot of fun even for older generations.

F1 Race Stars is a nice racing game, and it's appropriate for a 5 years old, I think.

Double Fine games like Psychonauts, Stacking and Constume Quest might be ok.

Maybe this?

Snuggle Truck

Zero Gear

Maybe a Sonic platformer

Too bad Beyond Good & Evil doesn't have controller support.

Rayman Origins is pretty cool.

Octodad
~he won't suspect a thing

GTA IV :D

Insanely twisted shadow planet

Hopefully your cousin can grasp the game quickly. I think a 5 year old can grasp this game. It gets a little bit hard on boss fights, also the size of the map can be overwhelming

Sideways - New York

It's basically Mario goes hip-hop.

Brothers: A Tale of Two Sons

dead space, you will have fun to look at him, maybe not him and wont talk to you again

Sonic & All-Stars Racing Transformed.

Kids love it, easy to play, has a bunch of Sonic and other cartoon characters - plus it's actually good for all ages (unlike many games that little kids enjoy).

Super Meat Boy, drop the kid in the deep end. You either break his spirit and turn him off gaming forever or he becomes some kind of gaming prodigy.

Ducktales: Remastered.
I haven't actually played it but I did play the original NES version, back in the day, and it was a lot of fun. The Steam version has full controller support.

GTA? ;D

Rapelay?

PixelJunk Monsters Ultimate and Shooter are good two player games suitable for all ages. Co-op play with controllers. Also, works on Linux.

Saw: The Video Game?
Just kidding... do something else, unless it's a multiplayer game, do something together with them.

monaco

Ikaruga, if your little cousin is hardcore.

Super Meat Boy !

Uh I dunno, I suggest just drugging him so he sleeps the whole time, so you can have a huge party with a lot of prostitutes. That's what my older cousin has always done when he had to babysit me back in the days and look how perfectly normal I am today.

BIT.TRIP RUNNER? Ive played the 2nd one and it doesn't seem too difficult for a child, plus its colorful and has a pickle man