Good grief....seems some have no idea what Fords '05 F350 SRW 6.0 diesel towing and weight specs are.
The OP doesn't have any reason to be paranoid...other than reading some members paranoid replies. In '05 Ford upgraded the SD line up with some big changes mechanically over previous year models.
Looking at Fords '05 body builders spec website shows the truck can tow a 12.5k lb TT with the std oem receiver hitch or 15k lbs with the optional receiver hitch. A receiver upgrade can be done cheap and quick...if its needed.
GN/5th wheel tow ratings are in the 16k+ range. Sure won't have a problem with any size TT rv trailer.
The OP truck has a 7000 RAWR that will be carrying all the hitch load and every thing else in the bed.
These trucks rear axle can weight in the 3000-3200 lb range leaving around 3800-4000 lbs for a payload in the bed.
Your trucks will be no where near maxed out for carrying TT hitch loads or pulling any TT.