You will not be able to tow a 10,000# tractor plus the trailer of the bumper hitch. Trust me, been there done that and have a broken hitch to prove it off my 2004 F-250 FX4 Short Bed Extended Cab. The hitch was rated at 12,000# and I bent it and cracked a weld 80% of the way through with 14,600# behind my truck from Pittsburgh to about 50 miles over the Indiana Ohio line. All this was on good roads like I 70 and US 35. Only 10 miles or less on non highway roads.
I found the broken hitch the next morning when I went to change balls from a 2 5/16" to a 2" ball to tow another trailer. I was lucky. The weld that broke was about 3" long and less than 3/4" remained. If it would have failed I would have had a mess. On the Reese Style Hitch if it fails the safety chains do you no good.
You did not list the year of your F-250, cab config, or if its 4x4 or not. I guessed with and used the info from my old truck, a 1999 7.3 auto 4x4 extended cab and my towing database says you are limited to 10,000# max off the rear hitch.
The only way you will be able to pull the load you want is to put a ball in the bed. By the way, its not a 5th wheel. They are what campers use. Equipment trailers use Goose Neck Hitches.
Chris