With a F150 that means unless you specifically order one with HD package your towing IS LIMITED to 5,000 lbs MAX per Fords towing guide
You need to re-read that towing guide..5K Max is without WD hitch per Ford towing as the F-250/350 SRW is 6K max.The difference in curb weight of my sons HD 2500 and my F-150 is like 300lbs and that's not enough to save anyone from anything or make any difference in a trailer pushing the tow vehicle around.
To the op...Try putting stuff in the back of the trailer if there is a door there instead of adding it to the so called payload of the vehicle.I sometimes put my generator just inside the door and or extra water/cooler etc instead of in the pickup bed.Easier to load and unload those items too.