A New Super Congruence Involving Multiple Harmonic Sums
  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. 
Liuquan Wang
math.NT