Oh I don't know, there are a few good finds for 5k that aren't beaters, but you do have to look carefully and know the right model years to look for. You're right about the Japanese makers, though. I'd put Honda, Mazda, and Subaru ahead of all the others.
Surprisingly, many of the car companies' finance arms will give you decent rates as long as you aren't in the credit basement. Several years ago, I managed to get an adequate rate from one of the Big Three on a car, even with a BK still showing. The promo rate at the time was 5.9% for 60 months, but they let me have it for 7.9%. Far better than the 14-16% I was getting quoted from the banks!
Go tomorrow and see if the maker won't give you a halfway decent rate. (It's the end of the month and the end of the sales year, so they're desperate to shift cars off their lots before they have to pay taxes on the unsold ones.)