Assuming rotations do not matter (i.e. if we number the seats {1,2,3,4,5} then

{A,B,C,D,E}  is the same as  {B,C,D,E,A} ) then the number of ways is:



  (5-1)! = 4! = 



 [ If the seat number that a person is sitting in does matter (say there is a special head-of-the-table seat), then there are 5! = 120 ways for them to be seated, basically the result above but multiplied by 5 for the 5 head-of-table seatings ]  

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