My 5 year old has been puking for the past hour. When should I be worried?

Dehydration. The main issue with vomiting is dehydration. If you truly can't stop them vomiting, then you should call your physician for help and assessment. However, if it's more a matter of a few intermittent vomiting episodes with some drinking in between, then you can work on properly hydrating them. If they get lethargic, or stop urinating, or just "look dry", they need attention for dehydration.