$\left\{ \begin{align}  & {{5}^{3}}=125=4(31)+1\overset{31}{\mathop{\equiv }}\,1 \\  & {{2}^{5}}=32=31+1\overset{31}{\mathop{\equiv }}\,1 \\ \end{align} \right.$ $5\times {{\left( {{5}^{3}} \right)}^{3n}}-7\times {{2}^{3}}\times {{\left( {{2}^{5}} \right)}^{2n}}\overset{31}{\mathop{\equiv }}\,5\times {{\left( 1 \right)}^{3n}}-7\times 8\times {{\left( 1 \right)}^{2n}}$ $=5-56=-51\overset{31}{\mathop{\equiv }}\,11$