What is the half life of Proscar and 5% Minoxidil respectively?

Proscar half life is 6 hrs (if you are young and have good liver function).   If you are older and your liver function is marginal the half life is longer ie 8 hrs.  Having said that, the effect of finasteride may last 5-6 days after stopping it due to the duration of its blocking effect on the receptors. Minoxidil topical is used once or twice a day.  That implies that the half life is about a day.  Some sources report 22 hrs. 

The half-life of finasteride is 4.7 to 7.1 hours per the pharmaceutical company's mechanism of action. There is a half life for minoxidil when ingested which is 4.2 hours. When minoxidil is applied topically the half life on the scalp is approximately 22 hrs and there is a small amount of systemic absorption.

The half life for Proscar (finasteride) is 4-6 hours in the blood spteam but it fixes to the receptors in the hair follicles for up to a week. Minoxidil is a topical, so it does not really have a half life unless you take it as a pill.