I have a 2014 Crew cab Silverado Duramax and I'm looking to purchase a fifth
wheel with UVW 12819 and GVWR 15500. I believe my towing capacity is
13500. Will it be safe to tow this fifth wheel.
Sounds like you would be legal and safe to tow just the empty trailer. You need to consider how much you load into the trailer for trips. Any time you approach or exceed the truck's limits you can endanger yourself and the vehicles travelling around you. If you do decide to purchase this particular trailer, please check out YouTube. Search videos on safe trailer hauling and be sure to travel at a safe speeds at or below the speed limit.
I think you need a 3500 truck.