Weigh your truck, with individual weights for each axle. Then you will KNOW what it can handle.
You're going to be sorely disappointed in what payload capacity you have left, going by the GVWR number. It's typically around 1300lbs! Seriously. Crew cab diesel 4x4 trucks are HEAVY.
If you want to tow anything appreciable in the way of a 5th wheel you're going to have to make the conscious decision to ignore GVWR and go by the individual axle ratings.
The typical 2005-ish 2500HD Chevy weighs about 2800-3000lbs on the rear axle with an empty bed. GRAWR is 6084lbs. That gives you around 3000-3200lbs of capacity on the rear axle.
5th wheel hitches weigh around 250lbs. That leaves you in the 2750-3000 range, but frankly I wouldn't push it unless you're absolutely confident in your driving and maintenance skills, and the trailer is something you absolutely cannot live without.
When looking at 5th wheels go by the GVWR of the trailer, not its actual weight. Use 25% of the GVWR as the pin weight.
Just off the cuff, a 5th wheel trailer with 10,000-11,000lb GVWR should work just fine.