jeeper....Straight answer would be if your F150 has enough rawr. A 7k dry weight which grows to 8500 lbs, maybe more, = 1600-1800 lb pin weight. Add 200 lbs for hitch/rails/etc......the truck has maybe 2000 lb siting on the rear axle. Now load the cab with all the people and other gear.
JMO if your truck has the 4550 rawr then your looking for around 2200-2300 lb payload on the rear axle. That size trailer will max out its load carrying capacity.
Ford markets the F150HDPP that comes with a 4800 rawr. Those numbers can give you a 2400-2500 lb rear axle payload and would be a good choice for under 10k 5th wheel trailers.