You have a 2016 3500 SRW with a payload of 4080# (is that what door sticker lists---Yellow sticker with 'Tire and Loading Information'
It will list YOUR trucks payload (Cargo Carrying Capacity)
15,500 GVWR 5th wheel.....
Using a 22% pin weight-----3410#
Your truck is quite capable of 'carrying' that pin weight
Check trucks RAWR and Rear Tire Max Load Ratings
Weighing truck fully loaded and camp ready is always best so you have real world numbers to work with
No need to look for a 13,000# 5th wheel
I tow 14K with my old 2007 3500 and am not over RAWR/Rear Tire Load witha 3000# wet pin weight
And my 2007 has lower ratings then your 2016
Is it time for your medication or mine?
2007 DODGE 3500 QC SRW 5.9L CTD In-Bed 'quiet gen'
2007 HitchHiker II 32.5 UKTG 2000W Xantex Inverter
US NAVY------USS Decatur DDG31