First the bad news. I don't think you will find anything out there, that would be dependable enough for full timing, in a diesel 1-ton, for $5,000.
A couple older diesel trucks to look for would be a Dodge, with a 5.9, or maybe an older Ford, with the 7.3.
If you were able to find an older GM, with the 8.1 gas, or an older Ford with the V-10 gas, they might work for you. Both were good haulers, but used a lot of fuel.
Good luck on your search, however, you may need to spend a little more up front, to get a reliable truck.
Jerry