You'll exceed the GVWR of your F-150 with even the smallest of the normal 5ers. You can probably tow something like the 19' Scamp 5er without being overloaded, if you load almost nothing in the pickup and very little in the trailer.
My 5er is a 25' with one slide and GVWR of 7,900 pounds. My F-150 is similar to yours, with 7,100 GVWR. Here is my CAT scale ticket when moving the 5er from Austin to my house a few months ago. The 5er was loaded to the roof with Darling Daughter's full-timer stuff, so it grossed about 8,000 pounds:
3300 steer axle (front GAWR 3750)
4680 drive axle (rear GAWR 3,850) so 830 pounds over the rGAWR
7,980 GVW (7100 GVWR) so 880 pounds overloaded over the GVWR
6800 trailer axles (7,000 combined trailer GAWR)
14780 GCW (17,000 GCWR)
Well below the GCWR, so no desire for more power to pull the big hills in the Hill Country.
My F-150 has the 6.5' bed and I did not have a slider hitch, so no problem with cab to trailer contact as long as I was going forward. And I made darned sure that I never had to back the trailer on that 350-mile tow through the Hill Country to my house. But your shorty 5.5' bed is a different story. You must have a sliding 5er hitch, or as a minimum a Reese Sidewinder pinbox on the 5er, and maybe both - if you want to have a normal RVing life with no fear of cab to trailer contact.