Almost totally agree with Lectrofuel. Your best bet is a minivan, full stop. Even those may not be in your price range without going tp a high mileage car. A good site to try is Truecar.com. If I use it in my area, a Toyota Sienna does not go below $5000 until you go back to 2008 and 175,000 miles and FWD. Toyotas do last a long time, but even at that point, rubber seals need replacement on the engine which will cost a few hundred dollars each time you replace one unless you do it yourself (I should know, every car I have owned at this milegae around this point needs them unless I do it myself, then the valve cover engine seal I did myself one time cost me about $60 in parts). For some reason, at that mileage there are a few cars available and all have about the same mileage and price.
If you raise that ceiling to $7000 you can get a much lower mileage Sienna that will be more reliable. For $6495 you can get in my area a 2006 7 passanger AWD Sienna with only 104,000 miles. This car will at this point would probably not need as much effort to keep on the road for at least a few years. A 2005 FWD 8 passenger Sienna goes for $5600 with 94,000.
So while I agree with Lectrofuel, for $5000 you are going to have to go pretty old and high mileage to get what you want which brings other issues. If you go up a litlte on price and are willing to go a little older on the model year, I would stick with Toyota for the most reliable option and get a lower mileage car.Unfortunately, for really long life unless you know what you are doing I would stick with Toyota still in this day and age.