Your really expecting a lot out of a gasser truck.
If you can find a V10 Ford 1 ton truck, then you are where you need to be.
You will not like the towing experience of the Chevy 6.0 with that much weight. Yes, it is capable of doing it, but not real well, and the mileage will be extremely bad.
Diesel is really the way to go for towing a fiver. The pin weight will also be well over 2000 lbs (figuring 20-25% of trailer weight) so you will run out carrying capacity in even a 3/4 ton truck.
I talk from experience having an 8900 lbs dry fifth wheel that had been towed with a Chevy 6.0 truck, now a Dodge Cummins diesel.
Steve and Vicki
2011 Dodge 3500 CTD Outdoorsman
2013 Columbus 320RS-ITS HERE!!