The Beauville $p^5$-group counting conjecture

Let $p$ be a prime. A Beauville $p$-group is a Beauville group whose order is a power of $p$. The Beauville $p^5$-group counting conjecture. For every $p\geq 5$, the number of Beauville $p$-groups of order $p^5$ is $p+10$. The source gives no resolution status or additional context beyond the assertion.