yes, $5k cash down will help alot. It will lower the loan to value ratio (amount of loan / value of car), and make it easier for a lender to grant the loan.
Wether or not it will help enough to actually get the loan depends on her credit AND financial situation.
Tell her to check her credit, make sure it is all accurate (see: credit boards forums), and get her scores
IIRC Capital One Auto has been awefully lenient with credit, and i’ve seen them (in two cases) write a $13k & a $18k loan (upto ~105% ltv) on used cars for people with solid income & credit scores in the 620-640 range on Equifax & Experian.
This little tidbit may help, but She (and you) need to do a little more research if she wants to get her credit info straightened out. It can be a pita, but is overall incredibly worth the time.