banjo..you have two weights of concern.
The biggie is (1) how much load the truck can carry and (2) how much can it pull down the road as in tow rating.
Looking at Fleet Ford towing guide shows a F350 DRW 6.0 diesel crew cab 2wd 3.73 axle has around a 16000 lb tow rating. Same truck with the tow boss package (4.30 gears) has a 18000 lb tow rating.
Fleet Ford says your truck has a 9000 RAWR. Many of these year model trucks rear axle may weigh in the 3300-3500 lb range which leaves around 5500 lbs for a payload. A 16k 5th wheel trailer may have 3500 lbs pin weight which leaves approx 2000 lbs for a hitch/gear and folks in the truck. The front axle will carry most occupants weights.
Most folks with trucks load them up and get their front and rear axle weight numbers so they know what numbers the truck can handle.
THe '05 can safely handle a 16k 5th wheel trailer.
We can't tell you what size trailer to get so use these numbers as a max.