Can i take zithromax again 5 days after taking it already knowing the infection isn't cleared by having unprotected sex three days later?

Probably no need: Azithromycin (Zithromax) is very long acting; it remains in the system for over 10 days after a single dose. Having sex 3 days after treatment isn't recommended, but the drug still in your system would prevent you from being reinfected with chlamydia. Maybe a different story if it's something other than chlamydia; ask the doctor or clinic where you were treated.