I've got an "outside-the-box" suggestion I guess --- but hear me out. First of all, $5000 can buy a lot of used car, if you go for the right models. The suggestions you've been getting of Sentra, Civic, other japanese econoboxes are prudent recommendations. But keep in mind that while these cars are generally reliable, they are also cars that are bought primarily by folks with not too much money, including young buyers who aren't too careful about regular maintenance. Surely you've seen the 24 year old woman driving the Corolla/Civic/Sentra/Ford Probe with the billowing smoke rolling out the tailpipe? She didn't check her oil. So, if you go for a small econobox type car, caveat emptor ... even a Civic won't last forever running dry. Also when these cars get to around 85k-100k, they start needing some parts. Wheel bearings, brake pads, tires, belts ... whatever it is, it is going to cost more on a japanese or german (vw) car than a domestic. (and by the way, avoid vw)
So, what kind of car is designed to run understressed, is generally cheap to maintain, has decent mileage (26 highway), cheap insurance (don't forget that), and is usually in good shape even though it's used???
Buick LeSabre. THere are tons of them on the market, cuz old fogeys love this car. Old wise fogeys. THey don't abuse them, they get the maintenance done on shedule, and since its not popular with young people, they are seriously undervalued on the used market. You can get a 1999 with about 75k miles and in beautiful shape for your $5000.
Think about it.