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What you are describing sounds like one of the front hubs is malfunctioning. I assume the vehicle is 4wd?
The hubs on the 2005 F250s are vacuum controlled and if the vacuum line leaks of the seal ruptures the hub will engage (lock in). With one hub locked and the other free it makes a terrible grinding noise.
Here is a diagram showing how the system works. The hub will probably need to be replaced if you can see the seal sticking out.
Yeah, it's probably going to need a new hub actuator assembly on that side.