I had this same issue with my pup when he was younger...it's pretty typical of GSD's or any dog with prey drive. My puppy was 12 weeks old or so, I put a drag line on him, next time my son ran by and he got excited I stepped on the line and his momentum corrected himself. He was little, so it only took two or three times with a "no!" command and it was done. With a 5 month old who has been self reinforcing this behavior by doing it over and over, you may need a higher punishment. I might put a pinch on a five month old (my dog was almost 60 pounds at 5 months), put the drag line on, and step on it when he jumped, allowing the momentum to correct himself. If you're all against the pinch on a "baby," you could put the drag line on him and give a swift backwards correction along with the momentum of him jumping, and give the "no" command. You don't need to over do it, your timing has to be just right, and you have to be consistent.
This is something I corrected/fixed as soon as I saw it, because I knew it would just get worse as the dog got older and bigger. You can't stop kids from running and yelling, it's what they do. My dog learned quickly and at a very young age, it was unacceptable for him to jump on kids.
I'm all about teaching a "place" command, and upping obedience. However, in this situation I want the dog to know that the behavior is unacceptable. I can't teach that jumping in a highly aroused state (chasing a squealing/laughing kid), is unacceptable by just putting the dog in his spot. I wanted him to know that it is NOT okay. Like I said, it was clear, concise, and we haven't had an issue since.
I have this funny picture of him jumping straight up next to my son, without touching him at all, but licking his face. He figured out he wasn't allowed to "touch" my son, so he'd jump straight up in the air NEXT to him and lick his face. In the picture you can see his feet are tucked up so he doesn't hit my son. Now he's tall enough that he can just walk by and lick his face lol. These dogs are too dang smart. :-)
"An excess of size is an unserviceable feature for breeding, his powers of endurance, his speed and the smartness of his movements suffer in all circumstances. Giants are never nimble."-Creator of GSD