Finding any vehicle in decent shape for $5K or less in the current market is going to be difficult.  At that price point, you're going to mostly see vehicles that are very high mileage, have mechanical issues, and/or have been in an accident or have had a title issue.  Possibly all of the above.

Also, while make and model still matter, at this price point how well the vehicle has been maintained (if at all) is going to be the most important thing.  You're going to be (metaphorically) panning for gold, trying to find a mechanically sound, at least somewhat reliable, vehicle amidst a lot of clapped out junk.

Lastly, I'd recommend you be prepared to put money into the vehicle and/or learn to work on it yourself to keep it going. Even a good find is probably going to need a fair bit of maintenance (belts, hoses, etc.) and some TLC.

whatever you can find, which won't be much for only $5k

I don't think you could even find an old AMC Eagle for that price at this point. You might be able to find an old Subaru but it would be pretty beat up and probably with blown (or soon to blow) head gaskets.