Pulled a 25' 5500lb camper + wood, water, bikes, etc with a 5.3 3.42 geared 2006 Tahoe for 5 years. It did everything I needed it to. Good WD hitch, brake controller, even distribution of junk you take with you between the camper the the TV, etc are important. Yes, you may be near the higher end of you truck's capabilities, but you will still be within them. Just know your limitations.
That said, I do now use a 2500 6.0 Chevy with a 4.10 gear and there is a huge difference, but I still go thru the same routines for setup regardless.