My girlfriend was tested positive for hpv, been together for 5 years and have never cheated, is it possible for the virus to be dormant all that time?

Yes: Before the vaccine became available in 2006 as many as 70% of college women attending health clinics tested sero-positive for HPV antibodies. Unless the strain involved symptoms like genital warts, the infection could lay dormant for decades.

Hpv: HPV infection is extremely common. Most people have no symptoms. Very likely she's had it for years.