The expression given is,
[tex]^5P_0[/tex]
We are to use the formula below
[tex]\begin{gathered} \mathrm{The\: number\: of\: possibilities\: for\: choosing\: an\: ordered\: set\: of\: r\: objects\: } \\ \mathrm{from\: a\: total\: of\: n\: objects}\text{.} \\ nPr=\frac{n!}{\left(n-r\right)!} \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \mathrm{Plug\: in}\: n=5,\: r=0 \\ \frac{5!}{\left(5-0\right)!}=\frac{5!}{5!}=1 \\ \therefore^5P_0=1 \end{gathered}[/tex]
Hence, the answer is 1.
