When is a 5th generation hiv test conclusive?

Six weeks (or officially 45 days). "Fifth generation" is a marketing term by the manufacturer. It's really a standard antigen-antibody (AgAb, 4th generation) test, and no different than other AgAb tests.

A positive result conclusive any time. A negative result 45 days after potential exposure is conclusive. Visit this site for info: HIV test window periods https://www.cdc.gov/hiv/basics/hiv-testing/test-types.html