Your tow rating is a max of 7,700 pounds if you have the 5.5' bed, or 7,500 pounds if you have the 6.5' bed. That means if your F-150 has nothing in it but a skinny driver, then the most weight you can pull without overheating anything in the drivetrain, and without being he slowpoke climbing grades, is 7,500 or 7,700 pounds.
If by "factory weight" you mean dry weight, then you're going to be overloaded with your F-150. And more likely you'll also exceed the 7,200 GVWR of your truck.
So you bought too much trailer for your F-150 to tow safely. Lots of folks "get by" with towing overloaded, so you won't be the long stranger out there. But realize you'll be overloaded, so drive very slowly and carefully.
The first chance you get, load the trailer and truck with everybody and everything that will be in it when towing. Drive to a truckstop that has a CAT scale, fill up with gas, and weigh the wet and loaded rig. Add the weight on the front and rear axles of the F-150 and compare to the GVWR of the F-150. Compare the total weight of truck and trailer to the 13,500 pounds GCWR of the F-150. Then drive accordingly.
Grumpy ole man with over 50 years towing experience. 2012 F-150 Lariat SuperCrew EcoBoost, 6.5' bed, Platinum White/tan, Leer 100XQ camper shell, Nomad Joey 196S TT, CarMate 7x14' enclosed cargo trailer, three other utility trailers, plus a retired 2000 Keystone Sprinter 25RKS 5er we rarely tow now. ProPride hitch on the TT. Reese Strait-Line hitch on the cargo trailer.