In how many distinct ways can $5$ people be seated around a circular table? (Two seatings are considered identical if each person has the same left and right neighbors).

Step 1: For circular permutations of $n$ distinct objects, since there is no fixed starting position (the table can be rotated), we fix the position of one person to break the rotational symmetry.

Step 2: The remaining $n-1$ people can then be arranged in the remaining seats in linear order:

Step 3: For $5$ people, substitute $n=5$:

So there are $24$ distinct circular seating arrangements.