If the 5 people sit in a row instead of a circular table, we would have 5*4*3*2*1 = 120 different combinations.

But since they sit in circular table if the people spin around the table without being in different position relative to each other does not generates a new position.

Thus if we denote the people by A, B, C, D and E the ABCDE, BCDEA, CDEAB, DEABC and EABCD arrangements are one and the same.

Thus there are 120/5 = 24 ways for the 5 people to be seated around the table.