It is entirely possible that you were infected with HPV before you met your current partner. It is very much a characteristic of HPV that it can lie dormant in the body either to remain that way or maybe get reactivated at some point; it can also be completely cleared by the body. If you test negative for HPV you either don't have the virus or it is dormant; either way, assuming you get regular screening, it shouldn't cause any problems. If you have an active infection, either newly acquired infection or because of reactivation, then a HPV test will give a positive result and there is the potential for cervical cell abnormalities to develop which may then become a cancer if not treated.
Regarding your question about whether it is a bad sign that your immune system hasn't cleared the virus if contracted 5 years ago, I'm not an expert but I would suggest probably not (insert disclaimer). The immune system is a complex thing and everyone is a bit different. There is evidence that smoking reduces the chances of clearing the virus so if you are a smoker then it's best to quit. After many years of normal smear test results, throughout my 20s, 30s and 40s, I was diagnosed with cc age 60y. In my case it is highly likely that I was infected with HPV during my 20s and had a persistent infection for decades - maybe it lay dormant all that time or for all I know maybe it went through cycles of reactivation and dormancy. I don't take it as a bad sign that my immune system didn't clear the virus, I don't think anyone really knows why some women get persistent infection and some don't and anyway I enjoyed very good health for all my life until cervical cancer reared its ugly head. Arguably, the bad sign was that I developed an attitude about smear tests and stopped attending for screening when I was 50y.
HPV testing does seem to cause a lot of anxiety and possibly even a guilt thing. But in fact it's a significant step forward in the world of medicine which enables improved monitoring of cervical cell abnormalities and should result in hundreds of fewer cases of cervical cancer in the UK every year in the near future.
Hope this helps a bit?