You know, now that I think about it, if you want to keep the truck, you are barking up the wrong tree with 5W. Ron's comment combined with the Trailer Life caution strongly indicates that a fiver would be a mistake.
Consider going to a conventionally hitched travel trailer. The limit of 8000 lbs will permit a pretty good TT. My 23' Prowler light weight scales in at 4650lbs and is very comfortable for two adults and a dawg.
The stability picture for TTs is way overblown. Properly set up, a TT is a stable easy tow, even with crosswinds and it tracks a turn a lot better than a fiver. They generally present a lower transverse section to a cross wind than a 5er. The way you properly set up a TT is to buy a good weight distributing hitch system together with a good anti-sway provision. I have run the Reese Class IV Dual Cam system for 16 years on two TTs and a big boat trailer. My current rig, a 1995 Bronco pulling a 23 footer, is thoronghly stable and quite comfortable to drive. Hell, my wife likes driving the rig -- a real blessing for a lazy husband. ;D
I am from Los Angeles. To go anywhere, I have to climb mountains or go thru Banning Pass, one of the windiest areas in the country -- it's a maze of windmills. The rig has handled 25 knot cross winds and beaucoup semis with no more trouble than any highsided vehicles under those conditions.
Good TT hitches include the Drawtites, Reeses, and Hensleys. You will pay a few bucks for them, but then 5er hitch plates are not free either.