your numbers are semi correct. GVWR is 12000lbs, then subtract the curb weight of the truck, which is 4700, this gives you 7300 pounds for max towing, even without getting into the payload, you're already going to be right at max towing when you start putting stuff in. It won't seem like you can't get 1k worth of **** into the camper.. but you will, even if you try not to. That aside though, lets look at the more important numbers. You did not list your GVWR ( which is the most important number ), so lets look at that, I believe yours is 7200 pounds, to get payload you subtract actual weight from GVWR in your case, 7200 - 4700 == 2500 , that seems awefully high, either the curb weight is wrong ( 4700 ), or GVWR is wrong ( the one I found on my own ), go get this number from the doorjam inside your truck. IF all these numbers are correct, that means you will be well within your limits of the truck on payload / carrying capacity, but will be right at the actual towing capacity. I've done this long enough to know though, the payload seems way to high IMO. That said, get the GVWR and let us know and we can tell you for sure.
The 5.3 Is an OLD outdated motor, that makes pretty horrible power either way, that putting 7k behind it in the hills will make you want to bite your nails off.
