No. of finite group (nonidentity)elements $x$ satisfying $x^5=e$ is a multiple of $4$

In general, if $p$ is an odd prime and $G$ a finite group, then $\#\{ g \in G: g^p=1\} \equiv 1$ mod $(p-1)$. Observe that the set includes the identity element. Proof (sketch): on the set $S=\{ g \in G: g^p=1\}$ define an equivalence relation: $g \sim h$ if and only if $\langle g \rangle =\langle h \rangle$. Then $S$ partitions in $\{1\}$ and equivalence classes of order $p-1$ (namely $\langle g \rangle -\{1\}$ for each non-identity $g \in S$).