S.M.
Personally, I have always found that if you are asking the question, then you should be calling. It never hurts to go to the pediatrician with a sick infant, especially with diareha or vomitting. It can't hurt and no one will think you are overreacting. Five months is very young, and they can go from bad to awful very fast at that age. So put your mind at ease and go. Odds are she is fine, and they will just advise on fluids and advise you what to look for in case she gets worse. That's what they are there for.
It could be bad teething, but she is really young for it. My kids did teeth around 5-6 months but most are later. Fever spikes and vomiting are very rare in my opinion so I would consider that it is not just the teething.
Obviously, i don't know if this is what you are dealing with, but my daughter had the flu about a month ago. You know, THE flu (swine). It is apparently really mild but pretty common right now - mild fever, decreased appetite, loose stools, discomfort, but little viral symptome ( not reallly a runny nose or cough). I don't know if they can provide a flu treatment if it's been a week and at that age, but worth checking. Good luck.