Like Masspike said, the figure you're missing is the GCWR, Gross Combined Weight Rating for your truck. This is the most the truck and trailer together can weigh alltogether.
Next in line is the GVWR, Gross Vehicle Weight Rating, the most the truck can weigh, including cargo, passengers trailer hitch weight, etc.
After that are the individual GAWRs ... Gross Axle Weights for each axle.
The 5th wheel hitch is directly over the truck's rear axle, so that's what will carry all of the trailer's pin weight.
On a bumper pull trailer, instead of the truck being nose up and tail down, the weight distributing bars on a equalizing hitch forces the truck back to a level posture. Doing this compresses the front springs on the truck and transfers some of the weight forward to the front axle instead of the rear axle carrying all of the trailer's hitch weight. The leverage also transfers some of the hitch weight back to the trailer axles.
The amount of weight that's transferred away from the truck's rear axle depends on how tightly you crank up the weight distributing bars, but for estimating purposes figure the rear axle of the truck will carry about 1/2 of the trailer's hitch weight and there will be about 1/3 - 1/2 of the hitch weight on the truck's front axle and about the same on the trailer axles.
Here's a link to the 2015 Chevrolet Silverado Towing Guide, in case you don't have it -
http://www.biggerschevy.com/towing-and-hauling-capacity/
The truck manufacturers don't make it easy to find the GCWR ... they'd rather publicize the inflated Tow Ratings that give them the most bragging rights. But we can infer the GCWR from the information in the Towing Guide.
And no, it's not 29,000 lbs (truck Maximum GVWR + the Maximum Towing Capacity).
The 2500HD with the Duramax diesel has a stated towing capacity of 17,900 lbs. The truck itself has a stated maximum GVWR of 10,000 lbs. and a payload of 3,501 lbs.
Subtracting the Payload from the truck's GVWR says the empty truck (including driver and fuel) weighs 6,499 lbs. Since the Tow Rating is calculated using the Empty Truck Weight, adding this to the stated Tow Rating of 19,000 lbs infers the GCWR is 25,499 lbs.
Now comes the tricky part ... since you can't exceed the GCWR, the most trailer you can tow is 19,000 lbs with an empty truck, or 15,499 lbs with a truck weighing in at the maximum 10,000 lbs GVWR.
Your Maximum Trailer Weight will fall somewhere between those numbers, depending on how much cargo you carry in the truck. Assuming, of course, you can distribute the load so the individual axle weights (GAWR) are not exceeded.
I'm going to go out on a limb and say you'll be perfectly fine towing a 7800 lb. 5th wheel as long as you stay within the truck's rear axle GAWR.
