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