If I have a pint of gin and 4 beers how long does it take to clear my system

Calculating BAC is an imprecise practice but it is safe to multiply the number of drinks consumed by 2 and then wait that many hours. A pint contains 8.5 standard drinks (US) so that would require 17 hours for clearance to BAC=0.

Clearance doesn't usually take that long but that is a safe time span.