Need more info. Make, model, year, does it have a tow package with hitch receiver, and auxiliary tranny cooler, all the details you have. You should be able to look up the tow rating in your owner's manual online.
Generally you are more limited in 5th wheel size than with trailer size. 5th wheels put a lot more weight directly on the rear axle (known as pin weight) and that becomes part of the cargo of the truck.
There should also be a curb weight somewhere on the sticker.
The info you listed tells nothing about the weight of the truck itself, so the gross weights don't give adequate info.