Getting a 3/4 ton vehicle in any kind of shape for $5K is going to be difficult, but not impossible.
We found a 7 yr old Dodge 3/4 ton, 2WD, 5.9L, tow package (tranny cooler, HD battery & alternator, HD springs, class 4 hitch) fairly new rubber, king cab and 8 foot bed with no rust and 80K miles on it for $5,600. We have been driving it now for 5 years and she still runs great and pulls our trailer very well.
Good luck on your hunt. We'll be in the hunt again in a couple of years, I would guess.