I played Mario & Zelda (1 & 2) on the NES when I was 5. I don't see why everyone thinks you need some "kiddy" game. All you need is a clean game. Granted, he is more likely to like some disney or movie tie in game than you or me, but I wouldn't exclude any other games.
Now, I don't think the X360 is particularly well suited for a 5-year old unless the parents don't care that he is playing T rated games. Off the top of my head games like Forza, or Madden would probably work (I'm assuimg they have an easy control mode). Any racing game with an easy mode would work. Banjo-Kazooie might work along with Sonic & Sega: All-star racing, or the Sega All-star Tennis. There are also the LEGO games but I believe they are E 10 but should be ok anyways.
If you go here you can select E and E 10 ratings to see which games are available on DVD.
Personally, I think the kid would be better off with a Wii just because of the larger selection of E rated games, but if he really wants to get a X360 there are more than enough good games to choose from.
