I'd say it depends on how far your towing, what kind of terrain you'll be towing it on,the ambient temp durring the tow, and your truck's equipment. If your going 30 miles on level road, you'll be fine, just drive very conservatively. However, a thousand mile tow thru the rocky mountains would most definitely kill the auto quickly, the truck just wasn't designed for towing serious weight.
a one time tow with a 5,000 lb. load isn't gonna kill the tranny, but making a habbit of it will certainly do so.
The 2 door 2wd automatic (with 3.73 rear) had the highest tow rating at 5,600lbs.
The 4 door 4wd manual (with 3.27 rear) had the lowest rating at 1,700lbs.
Assuming your's is 4x4 4 door automatic, you have two gear options: 3.27's good for 3,200 lb. tow rating. Or if you have the tow package, you will have the 3.73 gears good for 5,200 lb. tow rating.
Good luck!