I have been laid off for five months can my boss advance me mileage reimbursement and do I report it to unemployment ?

Yes your boss can advance you mileage reimbursement and yes you need to report it to unemployment. it shouldn't effect your benefits as you are genuinely owed mileage, but it always cover your back if you're clear and upfront with it,

No, he is not going to advance you any mileage reimbursement, since there are no guarantees that he will need you back or when he might need you back. If he gives you a loan/advance of any kind, you should report that to unemployment. Let them decide how to handle it.