All 2010 GM half ton crew cabs with 5.3L have 6-spd trans with 3.08 or 3.42 axle. Hopefully OP have the 3.42 as well as the HD trailering equipment. That gets tow rating around 9500 pounds. 10k+ is for the 6.2L and max trailering package. 6k dry is a good number and should tow well. Get a WDH with integrated sway control. The Trailer Tow button on the shifter does not eliminate OD, but does enhance towing experience as well as reduce transmission heat. Use it, plus I recommend M4, maybe M5.