Your 2013 F350 probably has a MAX 5th wheel towing rating of 15,200# which will result in a pin weight of roughly 3000# (+)
Check your rear tire MAX Load Rating @ MAX PSI on sidewall.
Will also need to check available payload capacity (that is what you actually have left over after subtracting trucks camp ready weight from trucks GVWR)
So if truck weighs 8500# (camp ready---all passengers, their stuff in truck, hitch in bed etc) and your truck GVWR is 11,500# that leaves you with 3000# before exceeding trucks GVWR. (Keeping in mind trucks RAWR & Rear Tire Load Ratings)
Tow ratings are high......unfortunately one runs out of payload before reaching tow rating.
The closer you are to MAX Ratings the less enjoyable towing.
The less one enjoys towing, the less one goes.