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The weight rating of 10,000 pounds is due to the limitations of the conventional hitch supplied with the original equipment tow package which you state that your truck is not equipped with. The safe operating range on your truck will depend on the weight rating of the hitch receiver you plan to use.
Your stock bumper is rated about half that or less @ 500 lbs tongue 5000 lbs total trailer weight.
Do not try to hang a trailer that heavy on a ball bolted to your stock bumper. You will need a frame mounted hitch receiver.
As far as the TRUCK being able to handle the weight, sure. I have safely towed heavier than that with my V10.
But without knowing what hitch is on your truck the above information is the best advice I can offer.
Tow packages often include a transmission cooler. Excessive heat due to towing can break down ATF fluid and negatively affect transmission life. If your 250 does not have one already, might consider adding it. I believe that is a relatively inexpensive mod.
If you look at an owner manual for this truck equipage as a crew with 3.73 axle, you will see a Gross Combines Weight rating of 17,000 lbs and a trailer weight of 10,300 lbs.
Of course you need supporting hardware for the full rating.
Trailer hitch and tonged/ball rated , Brake control unit in the Cab, trailer wiring to connect to the trailer and other approximate items you determine for the application.
Trailer max weight is calculated by subtracting the truck weight from the Gross Combined Weight rating.
That would be 17000- minus the truck loaded weight = the max loaded trailer wright.
For example 17000 minus 6000 lb truck = 11000 lb left for max loaded trailer weight of 11000 lbs.
The only difference between my example and the manual's max is the truck's loaded weight is an unknown unless you have it weighed.
Good luck.
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