Please don't take offense - you obviously know your boy, but I'd be very nervous about giving a five-year-old a semi-automatic firearm. I have a ten-year-old boy of my own, and he's fired my guns many times - always under extremely close (hovering over) supervision, but I only gave him his first single-shot pellet gun for his 10th birthday. I considered a bolt-action .22 at first, but decided the pellet gun would allow him to shoot more often, and be less likely to lead to flinching.
I've taken lots of boy scouts (12 and up) shooting, and I don't think a lot of them are ready for a semi-auto. I understand being anxious to get your boy into your hobby (I feel the same way), but I wouldn't want to be at the range with a 5-year-old shooting a 10/22 unless dad were physically controlling muzzle direction at all times. I'm sure many kids that young could physically point the rifle and pull the trigger - but is it realistic (or fair) for us to expect them to learn and practice safe gun handling 100% of the time?
I don't mean to be critical or tell you your business (especially when you didn't ask for opinions on this), but the thought of a five-year-old with a semi-automatic makes me nervous. And I've already learned by my own experience that it doesn't pay push your kids into your hobbies before they are ready.
Regarding the shorter stock, I'm sure there are many extras around from people who have replaced them. I'd ask at the gun stores or maybe post on a 10/22 forum.
Doug