I have a 2003 Silverado, 5.3L, extended cab, 4 x 4, 3.73 gear ratio. Max towing is about 7800lb, gross combined is about 11,500 lb. I bought a 28-1/2 ft, wood framed, bunkhouse model with no slides weighing 4600 empty, with 2000 lb (maybe more) cargo capacity. After the trailer and truck are loaded I tow okay enough. I am not towing mountains, and can keep my speed going up hills, but definitely have to work the gas pedal to find the sweet spot to keep the speed limit and keep from over reving on long shallow sloping hills.
Loaded for boondocking 80 miles from home, I am maxed out on weight. You're aleady maxed out before you even load your TV and trailer.
With a half ton, keep the trailer weight below 5000 lbs, you'll be a lot happier as long as you're not towing in the mountains.