Likely will do the job, my lame 89 F250 with a weak 460 and C6 auto. Did ok, with a 1986 28' King of the Road.
Keep in mind when calculating, GCVW with a 5er ONLY the 5er's axle weight is added, as the pin is part of the GVW of the TV.
So you are looking at 9,200#+ 6,800# = 16,000#
Not likely you are going to get 3,800# of stuff into the 5er, more like 1,500#.
ON EDIT: That owners manual, likely has a statement about frontage area, not to be exceeded.
I was never so happy when I got rid of my F250, 460, and got my Ram 2500 Cummins, difference of night and day. I will admit that my 460 was at less than 100%, and a regular cab, not worth putting money into to fix.