DO NOT USE gcwr less vehicle wt to get max tow rating! If you are at gvwr before loading a trailer, you have NO ability to safely tow a trailer! unless you can do this with no hitch wt in a safe and sane manner.
Take loaded truck with family on board, from gvwr, then take this number divide by HW % you need, you have max trailer you can tow. If you have 1000 lbs left over, 10% gives you a 10K trailer. If you need 20% for a 5w, you have all of 5000 total lbs of trailer capacity. This is the absolute best way to figure out how heavy of a trailer your rig can handle.
marty