Is it normal to have 5 hsv-2 outbreaks in the last 3 months despite using daily suppressants?

Probalby not herpes: HSV2 rarely if ever causes such frequent outbreaks. Once a month (12 per year) is pretty much the maximum, and most people with recurrent genital herpes outbreaks (due to HSV2) have them every 6-12 weeks. It is likely something else is responsible for the symptoms you are experiencing. See a doctor during one of those periods for examination and perhaps PCR testing for the virus. Good luck.