\(\hept{\begin{cases}5^{x+2}=25^y\\27^y=81.3^{x+4}\end{cases}}\Leftrightarrow\hept{\begin{cases}5^{x+2}=5^{2y}\\3^{3y}=3^{x+8}\end{cases}}\Leftrightarrow\hept{\begin{cases}x+2=2y\\3y=x+8\end{cases}}\Leftrightarrow\hept{\begin{cases}x=2y-2\\3x=2y-2+8\end{cases}}\Leftrightarrow\hept{\begin{cases}x=10\\y=6\end{cases}}\)