Where did you get your TV weight? With an F150 you’ll run out of payload before you get near the tow capacity. The best way to get good numbers is to weigh the TV fully loaded with people and gear as it would be on a trip. Then subtract that from the TV GVWR for your payload. If your GVR is the 7350# noted and the LOADED TV is 5832# and the LOADED TT weight is 6500# it should pull it OK. If any of those are dry weights you’ll need to get real weights and recalculate. At that weight, though, you will notice pulling mountain grades.