A 2000 or newer crew cab capable of pulling 7,000 pounds for $5,000 is a tall order. It will either have tons of miles, be beat to pieces, or both.
I would look for a GM with the 8.1L engine and Allison trans. However, for the budget you will probably be stuck with a 6.0 engine. It's still a very good engine but doesn't have the power of the 8.1.
Dodge trucks from the late '90s and into the early 2000's had problematic automatic transmissions. I had one that had to be rebuilt at 90,000 miles. Even when working properly I didn't like it. It never seemed to be in the right gear for the job. I manually turned OD on and off and shifted between 2nd and 3rd manually; basically driving like a 3 speed on the tree. If you get a Dodge I'd get a manual for sure.