$\begin{array}{l}
{15^5} - {5^8} = {\left( {5.3} \right)^5} - {5^8} = {5^5}{.3^5} - {5^8}\\
= {5^5}.\left( {{3^5} - {5^3}} \right) = {5^5}.\left( {243 - 128} \right) = {5^5}.118\,\, \vdots \,\,\,118\\
\Rightarrow {15^5} - {5^8}\,\, \vdots \,\,\,118
\end{array}$