If the math doesn't work for THAT trailer, find another trailer where the math works.
I have been going through this exercise for the past couple of years.
I just bought a 2016 F150 with 3.5 Ecoboost that is rated to tow 10,600 on the receiver and GCWR of 15,600. My GVWR is 6,900. Payload is 2,078 pounds. This is NOT the max towing package.
If I towed that 8,000 pound 5er I have 50 pounds to spare, and that include passengers, cargo and the trailer hitch. That is payload, no where near my towing capacity. I could still tow my 2,300 boat (full tank of gas) behind the 5er, and the hole package leaves me 50 pounds to spare on the GCWR.
The most important real number you need to know is the weight of your truck with a full tank of gas and you in it. Published truck weights may or may not include options and/or factor in a driver (150 pounds).
My actual truck weight with me, full tank of gas, and my two Shih-Tzu's is 4,800 pounds (curb weight).
There is a 5er out there your truck CAN pull. Happy hunting. My challenge isn't weight, it's length.