You do realize that there are some people (a lot of the ones fighting for health care) that can't afford it? I'm paying about $90 a month for the cheapest insurance my company offers. That on top of rent, car insurance, other bills, and student loans is the difference between me eating like a normal human being or having to eat ramen noodles for dinner every night. I don't have any kids either, so imagine someone who works the same position as me and is a single parent with even more bills. It isn't a matter of "not bothering to pay" but more "don't have the means to pay". Like anything else there are people who want to abuse it, but assuming that is the bulk of those fighting for it is a bit absurd.
But this thread really shouldn't be a discussion on such things.
$5,000, while a lot of money, really shouldn't be that hard for her to come up with. Add to that the fact that you can generally set up payment plans with them so that you don't have to pay it all up front.
As for the car, it depends on how she payed for it. If she bought it outright then I see no reason why she couldn't trade it in for an older model and have money to pay off her debt. However, if she got financing then generally the financing body will only loan you what the car is worth, the blue book value. Say you are allowed a $18,000 loan but the car is only $16,000 then the bank will only give you the $16,000. So if she were to try and to downgrade in order to have extra money there could be some potential complications with the loan.