The Everest 293P is a full-sized 5th wheel, and well-beyond the capacities of your current truck.
The dry hitch weight (approx 2,375 lbs) will likely be in the 2700++ lb range once loaded to travel.
The following specs are for a 2007, but I'm sure the 2005 is 'similar'.
293P Specs (2007)
Dry/Shipping Weight 9,910 lbs
Carrying Capacity 2,790 lbs
Dry Hitch 2,375 lbs
Length 32' 10"
GVWR 12,700 lbs
http://media.rvusa.com/library/07_Everest_FW.pdf
Look for another truck!! Most likely a 350/3500 SRW, with a 'minimum' available payload for the loaded
pin weight, plus passengers, plus any cargo & a 5th wheel hitch.
Terri, the Chevy co-pilot