Keep in mind that the Gamecube is the 1st system that Nintendo has produced that can't seem to make them any money. While I don't mean to infer that they are about to pull the plug on the system, Sega pushed and promoted their Saturn up to the very end but after losing so much money, the company that used to be Number 1 in the industry (Genesis pulled ahead of NES & SNES), they now are a software company. The Gameboy has run strongly and still defeats all of it's competition so Nintendo won't abandon that.
Between the X-Box & PS2, for a 5 year old, I would go with the PS2. We own all 3 and DD6 likes the games better and the controller is better suited to smaller hands. Now, if it's really Mom or Dad that the system is for, the decision becomes more difficult. We look at lots of factors when choosing games that are available on all systems. Graphics are better on the X-Box but the control is better on the PS2.
The PS2 will play DVDs out of the box but the XBox needs a separate remote (eBay for less than $20) w/shipping).
The PS2 needs a memory card to save games but the XBox has a built in hard drive. The hard drive also helps haves to load faster so there's less time in between levels.
Supply is good right now and they don't predict that there will be shortages like in the past so I would wait 'till closer to Christmas for a possible (although denied by both companies) price drop or better bundled package.
Either way, they are both great systems. Look at the games that are available (remember that the PS2 can play the old regular Playstation games as well and some of these can be had for absolute bargain prices). Listen to any information that you get from the store clerks but remember that there may be internal pushing towards one system over another (I worked in one of the bigger gaming specialty stores for 12 years and it DOES happen).
Good luck & have fun!