I added 250 lbs since you said you didn't have hitch and this is what I come up with.
You have 2,590 lbs. of payload capacity. Fifth wheels typically have 20% - 25% pin weight which gives you a maximum loaded
trailer weight of 10,360 - 12,950 lbs.
WARNING that is loaded ready to camping weights not the weights posted on the websites or on the 5er. Best to add 1000 to 1500 lbs ( more depending on your how much you plan to bring camping) to the Dry Weight/Shipping Weight and use those numbers. You still need to say within you towing limits also.
Link to the numbers --- Towing Calculator after getting weighed - Towing Planner