Hey 1ed, I have extensive experience with that situation.
I had a 1999 Tahoe with the 5.7 and we pulled a trailer weighing 5000+ pounds.
We pulled that thing from the coast to the smokies here in NC and that truck was a BEAST! Never let me down! Never!
I finally sold that beast with 275K on the odometer and it had zero issues.
You don't mention a hitch, so I recommend a good weight distributing hitch. I used an Equalizer and was happy with it.
I also recommend adding s set of Timbrens to the rear end. These SUV's are soft in the rear and the Timbrens worked perfectly for me in this application.
Good luck in your travels and let me know if I can help.