Chapter 10 Counting Methods and Probability - 10.1 Apply the counting Principles and Permutations - 10.1 Exercises - Problem Solving - Page 689: 71a

$24$

We have $5!$ arrangements, but each of them is counted $5$ times. This is because we can "rotate" each arrangement by $1$ clockwise and we get the same arrangement but after $5$ rotations we get back to the original arrangement. Hence the answer is: $5!/5=4!=24$