Get the truck weighed with all occupants in that will travel when towing, also whatever will be in the bed. Add 150-200lbs for a hitch. Once you get the weight, the rear axle weight rating (GAWR) is going to be a limiting factor + the max weight the tires are rated to carry (usually around 7500lbs). Once you have a valid weight number to work with, and an axle weight to give you the what is already on the axle, then you can use 20% (pin weight) of the GVWR of any trailer you are considering. If the pin weight + the axle weight/tire rating are = to or more than the RAWR/tire rating, you need to find a smaller fiver. The GVWR on your truck is probably around 11400, but the rear axle and tires are the real limit on a single rear wheel truck.
RAWR = +/- 7500lbs; rear axle as weighed =4500lbs. 7500 - 4500 = 3000. This is the maximum pin weight you should consider. At 20% of GVWR, the max trailer you can consider is 15000. And this will be pushing it a lot. DO NOT WORK with any 'dry weight' numbers a mfg will list, not reality.
A lot of people tow heavy fivers with 250s, but should you do it? Your choice, at least you have a 350 to help with the numbers.
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired