Solve for x:

$\left(\frac{2}{5}\right)^{2 x-2}=\frac{32}{3125}$

$\Rightarrow\left(\frac{2}{5}\right)^{2 x-2}=\frac{2^{5}}{5^{5}}$

$\Rightarrow\left(\frac{2}{5}\right)^{2 x-2}=\left(\frac{2}{5}\right)^{5}$

$\Rightarrow 2 x-2=5$

$\Rightarrow 2 x=5+2$

$\Rightarrow x=\frac{7}{2}$

Hence, $x=\frac{7}{2}$.