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Using the box method, 
__ __ __ __ __

In the first position, five different people can be placed.
5 __ __ __ __

In the next position, since we've already placed one person in the first position, therefore we are only left with 4 people
5 4 __ __ __

Continuing the pattern, we get
5 4 3 2 1 

Therefore there are 5! ways possible.  120 ways.

You can also use permutation, etc. to solve this.

Hope this helps :)
p.s. If there is a part of my solution that you did not understand, please do not hesitate to contact me and I'll be more than glad to explain it to you thoroughly
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