There are two numbers: towing capacity, which is how much weight the truck can pull, and payload, which is how much vertical load the truck will carry.
The truck you're looking at should be able to pull the trailer, but the payload is insufficient. The 2500 probably has a payload around 2700 lbs. As a rule of thumb, you should figure around 20% of the total weight of the 5th wheel will be on the hitch. A 16,000 lb 5th wheel would have around 3,200 lbs of pin weight sitting on the hitch. If you have the on board generator and washer/dryer, you may be closer to 3,500 lbs. In addition to the pin weight, the truck payload has to handle passengers, pets, tools, weight of the hitch, bed liner, bed cover, and anything else you put in the truck.
We have a GMC 3500 SRW pulling our Rushmore. It pulls very nicely and handles the pin weight just fine. But many owners recommend getting a dually for better stability and increased payload and towing margins.
A few owners are pulling Landmarks with 2500s and have added airbags to the truck to keep it from squatting. That levels things out but doesn't add payload capacity.
You can find out more at
Fifth Wheel Safe Towing.