My 5 month old baby has been vomiting for about 3 days now. Has had no fever or any other symptoms. Should she see her doctor?

Yes. A 5 month-old baby is pretty young, so should be seen by the doctor to see what may be causing the vomiting (maybe an ear infection, a bladder infection, a stomach/intestine infection, etc.). If no serious problem is found, the it is likely a viral stomach flu, but one cannot tell without an exam. The doctor will also assess the baby's hydration status at the visit.