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If the gvwr of the truck is 11,500, that means that the weight on the truck axles is 11,500. Each axle has a rating. You can not overload either axle. GVWR of your truck has nothing to do with the total trailer weight, but the weight on the hitch adds to the weight already on the rear and front axles. Weigh each axle with the 5th wheel attached to be sure that neither axle weight is overloaded. I'm sure you will find that you will have plenty of extra carrying capacity.
Towing capacity is a totally different thing. I already know that a 3500 Chevrolet srw will tow well over 14,000 pounds. My 2018 srw is rated to tow more than 17,000 pounds. You probably have way more truck than you need.
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