  Let $G$ be a finite $p$-group of order $p^n$. It is known that
$|\mathcal{M}(G)|=p^{\f{1}{2}n(n-1)-t(G)}$ and $t(G)\geq 0$. The structure of
$G$ characterized when $t(G)\leq 4$ in \cite{be,el,ni,sa,zh}. The structure
description of $G$ is determined in this paper for $t(G)=5$.
