Problem 44717. Five Fingers

A little girl has just learnt how to count from 1 to N using the five fingers of her left hand as follows. She starts by calling her thumb 1, the first finger 2, middle finger 3, ring finger 4, and little finger 5. Then she reverses direction, calling the ring finger 6, middle finger 7, the first finger 8, and her thumb 9, after which she calls her first finger 10, and so on.

We will index her left hand from the thumb to the little finger in the order finger 1 to finger 5. Now, if she continues to count in the described manner, on which finger index will she stop for a given N?