If you're looking to purchase it from your mom, would she accept payments or does she need the cash out of the car? You can eventually get the title in your name once the lien is satisfied.
Side note - just say NO to the X5, lol! You will end up over-extending yourself if you can get a loan to finance. I know because I was just looking at the same car, same model years. The salesman was very honest about their resale value, how expensive they are to repair, maintain, etc. I make quite a bit more in income, just have a rent payment, no CC debt and minimal bills, and I still couldn't make the financing work without a big downpayment being required from every single lender. Just make sure you are realistic on how much a bank is going to lend you with such a limited recent credit history (less than 2 years) - even so they are most likely going to charge a decent interest rate on a used car if your scores don't get up there (look at your auto scores too, not just fico 08's).
Just my advice because I just went through it yesterday, you may be able to get a better deal or financing but you need to take a look at what you can afford, you're going from a possible loan under possibly $18K for your moms car versus $35-$40k on a used X5 (I was looking 2013 or newer too) - big, big, big difference for your first car loan after all the credit problems. Be wise, keep telling yourself it is just some metal on wheels to get you from point a to b, you can't live in it, you shouldn't eat in it and it won't ever appreciate, it's value is only gonna go downhill! Oh yeah, and premium gas is expensive!
