If you are looking at a 15,000# 5er you will have a pin weight of 20% plus or minus a little so a 15,000# trailer means you will put 3,000# give or take, into the bed of the truck. So if you add people, gear, firewood, fuel what ever in the truck you still need to have 3,000# of cargo capacity left for the trailer. So I'd say look for a truck with a cargo capacity of 4,000# minimum.
Since trucks normally run out of cargo capacity before they run out of towing capacity this will probably simplify your search.
Also know that after 2004 the truck ratings took a jump so a 2005 truck has a higher rating than a 2004 and the new trucks are in a whole new class.