Am I Calculating This Correctly?? Silverado 1500

I have a truck that weighs 7300 pounds, a one ton diesel. I haul a fifth wheel that weighs about 8500 pounds. I wish I had more truck, better acceleration, much better brakes too. Uphill and downhill are my shortcomings, but flat and level it seems fairly well balanced in all the conditions I have encountered. Combined, it is 42 feet long.

You have a light truck, a heavy trailer, and a family depending on your choices. I would really like to see you with a bigger truck.

Is there any way to increase my towing capacity with changing out the gear box for a 4.10 and/or beefing up the Springs and brakes?

With that gear ratio, you will be best to stay in flat country. I had one in Colorado and I was going up hills (not mountains) at 10-15 mph. Not fun or safe!

The specs on a light crew cab 1500 (LT) show:

weight 5333
payload 1740

The door sticker will surely be higher weight and lower payload.

I've had a Silverado. Avalanche and Tahoe with the 5.3 and now the 3.42 rear end. I love the engine for it's reliability but it's a weak engine for towing. I have towed a 4,000 pound (real empty weight) and the same trailer weighing 6000 pounds. The 4000 weight I've towed long distances and the truck did pretty well. When weighing 6000 pounds I towed it locally and would not want to tow it a long distance or up mountains. I think the truck would do it, but I would be a nervous wreck.

With that gear ratio it won't tow great, but it is possible. A good WD hitch would help.

No. You need to know the payload rating of your truck, found on the tire inflation sticker inside the door jamb. Then, subtract the trailer tongue weight, family, and any cargo in the truck. Also subtract 100 lb for the weight of the WD hitch. If you have anything left over, then you are not over your payload.

The tow rating number refers to only the trailer weight. With a half ton, you will exceed the payload limit before you reach the tow rating number.

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.

You don't include tongue weight for GCWR. I would say your truck is good to go.