Negative 4th generation ("duo" or "combi") tests are conclusive any time 4 weeks or more after the last exposure. There is no second window period; that's an urban myth (see the third thread linked below, in particular the follow-up comments December 25). Your negative result at 5 weeks proves without doubt you do not have HIV and you do not need further testing. You can safely have sex with your partner. However, if you would like the additional reassurance of a negative result at the official interval, feel free to have another test at 3 months. Personally, I wouldn't do it and I don't recommend this to my own patients.
@ erayfobi
