Answer
See below.
Work Step by Step
The number of ways to select the first performer: $5$ (any of them can be apart from the one who wants to be the last)
The number of ways to select the second performer: $4$ (any of them can be apart from the one who wants to be the last and the already selected first singer)
The number of ways to select the third performer: $3$ (any of them can be apart from the one who wants to be the last and the already selected first and second singer)
The number of ways to select the fourth performer: $2$ (any of them can be apart from the one who wants to be the last and the already selected first and second and third singer)
Then the fifth performer is the one who is not the first, second, third, fourth or last.
The last singer is fixed.
Number of different ways to schedule the appearances:$5\cdot 4\cdot3\cdot2\cdot1\cdot1=24$
