I'd get a real stick for him, although at 5, even a kid size stick may be too big. If your jump stick has a non-leather tip that is. Or convert a jump stick to a leather tip. My 5 yr old girl has been going up to my son's league with us and is having a blast, she shoots with just a shaft from an old Action kid stick my son used. She has a tough time holding the stick to shoot due to the weight of the butt end, even though the shaft is a bit too small and light also.
You may want to explain some rules to him, but don't try to actually stop him from playing around his way. The reason you want to go over the rules now, if he plays for a while as is, and then you or someone else tries to teach him a different thing (like, you can't move the ball, or you need to hit this ball first), he'll be liable to get stubborn, angry, etc...
If he at least knows that there are "real" rules when he starts, it will be easier to transition into playing the right way.