$\begin{align}  & {{5}^{2(x-1)}}\times {{5}^{x+1}}=0.04 \\ & {{5}^{2x-2}}\times {{5}^{x+1}}=\frac{4}{100}=\frac{1}{25} \\ & {{5}^{2x-2+x+1}}={{5}^{-2}} \\ & {{5}^{3x-1}}={{5}^{-2}} \\ & 3x-1=-2 \\ & 3x=-1 \\ & x=-\frac{1}{3} \\\end{align}$