  Let ${\mathcal{P}_{n}}$ denote the set of positive integers which are prime
to $n$. Let $B_{n}$ be the $n$-th Bernoulli number. For any prime $p\ge 5$ and
$r\ge 2$, we prove that \begin{equation}
  \sum\limits_{\begin{smallmatrix}
  {{l}_{1}}+{{l}_{2}}+\cdots +{{l}_{5}}={{p}^{r}}
  {{l}_{1}},\cdots ,{{l}_{5}}\in {\mathcal{P}_{p}}
\end{smallmatrix}}{\frac{1}{{{l}_{1}}{{l}_{2}}{{l}_{3}}{{l}_{4}}{{l}_{5}}}}\equiv
-\frac{5!}{6}{{B}_{p-5}}{{p}^{r-1}} \pmod{{{p}^{r}}}. \end{equation}
  This gives an extension of a family of super congruences found by Wang, Cai
and Zhao.
