Well, if they overpaid and your mom didn't notice... she should've noticed, that's how it usually works.

They thrive on such mistakes of theirs.
I'm not saying it's her fault, because it's theirs. But if she didn't notice and spent what wasn't hers in the first place, there is no way they will let it slide. I know they wouldn't let it go in Poland. Especially $5k is a lot of money. I'd ask them to split the debt into installments. Unless there is some law in the US that allows her to avoid paying it back.