It is a simple question easily resolved. Your truck has a max cargo limit on what it will carry. Regardless of the motor or gearing.
About 12 to 13 % of the trailer weight is transferred to the tongue. That means before you add anything to your trailer you have about 1000 lbs. on the tongue. Not much cargo capacity left for family, toys any gear.
In the end you will find an F-150 is best suited for a 5000 lb. dry weight trailer once it and the truck are loaded for the road.
The scales do not lie or exaggerate.
When I doubt, rent what you want first.
Good luck