Non-Abelian Order 10 Group has Order 5 Element/Proof 2

Theorem

Let $G$ be a non-abelian group of order $10$.

Then $G$ has at least one element of order $5$.

Proof

As $10 = 2 \times 5$, $G$ is a non-abelian group of order $2 p$, where $p$ is an odd prime.

Hence this is an instance of the result Non-Abelian Order 2p Group has Order p Element.

$\blacksquare$