Positive pregnancy test after 5 days of intercourse or from prior intercourse session?

Likely from prior. Most home urine pregnancy tests are sensitive enough to detect HCG levels about 2 wks post-conception. HCG levels double about every 2 days, but these levels vary from woman to woman, and what time of day the test is performed (early morning is best), so the test it may turn positive earlier for some women. It is more likely that your test was positive from prior sex.