I tow with and 1997 1500 Suburban. 5.7 Vortec, 3.73 gears, 33" tires, tow package.
Trailer is rated at 5200lbs dry, 6500lbs max. Normally tow with a little water in the tank and 4 people on board, plus your normal camping load out. I have towed with 6 people on board and all the stuff needed for them, no real problems but also no mountains on that trip. :)
Since I don't have tow haul, I lock it out of overdrive whenever I am towing.
Usually I stick between 55 and 65mph with the cruise set and have no problems. On steeper hills I may slow to 50, on the worst hills it would downshift to second and turn around 4k rpms.
In second gear it would have no problems maintaining even 60 if I wanted it to, but I normal just slow down a bit and try to keep it in 3rd.
I love this truck for towing our camper. 50 gallon fuel tank, long wheelbase, plenty of room.
My father in law tows a slightly smaller camper with a 5.3 Tahoe. He just sets the cruise around 60, turns on tow haul, and lets it do its thing. He has been running it this way for the last 2 years at least.