5 week old puppy started vomiting her formula and then yellow bile what should i do?

Vet, vet, vet! A puppy at 5 weeks isn't (and shouldn't be) even weened off their mother, why the heck is it being fed formula? Also, a puppy at 5 weeks hasn't even had their puppy shots yet, thus making them vulnerable to many puppy illnesses that can potentially kill them if they are not treated asap. Instead of waiting around on the computer, call up an emergency vet and take the puppy to them asap, and take the puppy's litter mates and mother if they're in your possession to make sure they are healthy as well. Good luck.