Young ones are pretty active - it sounds normal for a 5 inch baby. I'm not too sure on the colour change thing, as I don't have any white axolotls, however I find that my big boy's red gills get brighter when he's active and playing around - also after he's had a nice big juicy worm to eat! So I wouldn't worry too much about it. Make sure you don't have anything sharp in the tank that it can hurt itself on - sometimes they work themselves up too much and can damage their delicate skin and gills on rocks, cheap plastic plants, tubing and air hoses as well as filters and stuff. Smooth edged rocks and plastic plants are fine, just make sure they are not sharp in any way.
If you want you can actually play games with you axi - I do!!! However I over did it when I was off work for a few weeks - now when ever I come into the room they want to play a game, and for me to feed them!!! CRAZY!!! I always give in cause they look so cute when they beg!!!