2013 Chevy Tahoe / Forest River Cherokee Grey Wolf 23DBH

You are probably rated for around 8100lbs towing. I had a 2003 1500 long bed with the 3.42 rear end, and I towed a Grey Wolf 28bh. The weight of the 28bh is basically the same as yours.
With a weight-distribution hitch, the truck had no issues pulling the camper around (Ohio).

However, I did take it down to TN and over to MD and back. It wasn't fun. 2nd gear up the mountains and 35-40mph.

So, if you are towing in a flat or moderately hilly area, you are fine. Otherwise, consider something with a 6 speed tranny.