It would be better to look at the GVW for the trailer than the dry weight. The reason is, unless you're towing it home from the dealer, you won't be towing dry. You'll have food, clothing, dishes, towels, bedding, TV(s), etc. Some say people add about 1500-2000 pounds of 'stuff'. Having said that. If you divide the pin weight by the dry weight, you get about 18%. If the trailer was loaded evenly and the pin weight stayed at 18%, what would the pin weight be? (Norm for a 5er is 15-25% of trailer weight).
Now, if you have a camper package, do you have airbags to help hold that up? If so, it will help hold up the truck. But, you could still be over the rating for the truck.
Check out this website:
Look in the area of Pages 16-21 particularly, the F250/F350 pickups under the 5th Wheel towing section.