The circular permutation of n items is given by the formula (n-1)!. For our case of 5 things taken 5 at a time, we can apply this formula.
Here, n is equal to 5. So, we can calculate the circular permutation as follows:
(5 - 1)! = 4! = 4 × 3 × 2 × 1 = 24
Therefore, the circular permutation for 5 things taken 5 at a time is 24. This means that if you arrange 5 distinct objects in a circle, you can do so in 24 different ways, taking into account that rotations of the same arrangement are considered identical.