Gonna be PRICEY to pick up many of the Gamecube classics.
I'd say you're better off grabbing a cheap Wii, softmodding it (relatively trivial) and then just downloading isos to play via USB to be honest.
Good gamecube only games:
Super Mario Sunshine,
Chibi-Robo,
Wario World,
Eternal Darkness,
Wave Race: Blue Storm,
Mario Kart: Double Dash,
P.N.03,
Luigi's Mansion,
Donkey Kong: Jungle Beat (One of the best 2D platformers around, needs the bongo controller),
Paper Mario: The Thousand-Year Door,
Star Wars Rogue Squadron II: Rogue Leader,
F-Zero GX.
Good Gamecube games with enhanced Wii/Wii U releases that might be preferable:
Metroid Prime & Metroid Prime 2,
Pikmin & Pikmin 2,
The Legend of Zelda: Twilight Princess,
The Legend of Zelda: The Wind Waker.
Good multiplatform games on gamecube:
Resident Evil 4,
Burnout & Burnout 2,
Viewtiful Joe,
TimeSplitters 2 & 3.
Killer7,
Ikaruga,
Skies of Arcadia Legends,
Second Sight,
Prince of Persia Sands of Time trilogy,
XIII,
Beyond Good & Evil,
Spider-Man 2,
Incredible Hulk: Ultimate Destruction,
Alien Hominid (USA only),
Metal Arms,
Billy Hatcher and the Giant Egg,
Soul Calibur 2.
Not sure which games might be most appealing to a 5 year old, but I have bolded the ones that are probably inappropriate.