Since there are a total of 5 runners, there are 5 possibilities for 1st place. The possibilities for 2nd place are 4 since there are only 4 runners left. For the 3rd, there are possibilities of 3 runners. For the 4th place, there are 2 possibilities and 1 remaining possibility for the 5th place. Multiplying all the possibilities will give you the total number of different orders that 5 runners can finish the race.
Total number of different orders = 5 * 4 *3 * 2 * 1 = 120
You can confirm this using tree diagram.