Your misreading thonhs. Max TRAILER WEIGHT is 15,100 poumds. NOT maximum fifth wheel weight.
Pull trailers usually place around 12% of their total on the vehicle. Fifth wheels drop approx 20% directly on the rear axle.
So to get a reasonably accurate fifth wheel towing weight number, go to the scales and weigh your truck loaded ready to travel. Be sure to get accurate rear axle load weight. Subtract the scaled numbers from the drivers door sticker GVWR and RAWR. That is your absolute max payload and still be within the mfg certified weights.
In your hypothetical fivers numbers it appears that you will drop around 3000 poumds directly on the truck. But that does not cover the hitch, another 150 to 250 pounds. Since mystical dry weights are meaningless, I suggest you instead go find the fivers GVWR and use that number.