Prove largest positive integer dividing a and b is 1

Hey everyone, I can't figure this out (I don't understand how to get there), it seems simple but it is just frustrating the life out of me!

Let a and b be integers such that 5a - 3b = 1. Prove that the largest positive integer dividing both a and b is 1.

My professor told me to start by saying "Let d be a positive integer that divides both a and b, then d divides ?"

It doesn't really help me as I have no idea how to approach this.

Any help/explanation would be fantastic!