This is not a criminal case it is a business law issue, when you hand over the keys you pretty agree to everything. Look for signs saying we are not responsible, i'm sure they have them. However, depending on the amount of the claim if its low just pay for it, if it not you can sue but its probably won't be worth your time. The 5k claim is bogus, 4000 in labor? might wanna sue them!
While a business can't absolve it self from negligence , it will be hard to prove and comes down to basically if they want to settle it or not.
What to take away from this: Check before accepting your vehicle. or never valet.
Not a lawyer, but I took business law