The F250 may be able to carry it, you will be over your GVWR, based on the dry hitch and your stated payload. Should be within axle ratings, no problem.
You real issue will be if you have enough engine to move that tall 5er. any wind will likely have a big effect on speed, and mileage. You will likey see issues with climbing hills. I don't think you will enjoy the experience.
You also didn't mention gear ratio, without 4.10's not likely to be fun at all.
You either need a smaller lighter 5er, or bigger engine. You could look for a V10, a SRW 350 would allow you to tow within GVWR if that is important to you.
I don't worry about GVWR too much, axle and tire are what really counts and I will not exceed either. If my TV needed bags or Timbier's I would also be rethinking my 5er. I do have more than enough engine to move my 5er, so that is what you need to keep in mind.