I towed with a 5.3 liter Suburban from 2004 to 2007 with a 26 foot travel trailer. The 5.3 liter is very poor towing anything above 5000 lbs dry weight.
Your experience will range from constant shifting in head or side winds or going up any slight grade. Towing in the mountains or steep hills will pull you down to 30 to 50 mph with you foot pushing the gas pedal into the floor.
You need to be extremely careful in your selection. Do not believe a salesman who will tell you anything to get you to buy.
I ended up upgrading to a Chevrolet 3500 dually pickup with a turbo diesel. It tows my 35 foot TT like it is not there.