The GBA would probably be best. Any of the current controllers would probably have too much going on for a 5 year old. I thought about Ape Escape, VJ, etc, and I think they'd all be too complex.
The GBA, on the other hand, is perfect. There's various Disney and Cartoon Network games for the system that would be perfect and would probably star a character they're familiaer with.
GameDAILY actually publishes a family guide that was created to answer this VERY question for those that don't really game much themselves:
I disagree. They're fine in subject matter, but no 5 year old will get much enjoyment out of Pikmin, Mario Vs. DK, Animal Crossing, Paper Mario, Metroid, or most of nintendo's other games this gen. They're too complex or require too much reading.
We're working on classifying reviews by age for early in 2005. I know that doesn't help so much now, but all reviwes have an age range on them there now. There should be a Holiday Guide starting sometime this week too.
My three year old can play and enjoy Kirby Nightmare in Dreamland, Mario Sunshine, Mario vs. DK, Sonic games, and he can actually beat me in Pushy Penguins in Mario Party 5.
My seven year old can play anything except fighting games... he just doesn't like them.