Get the same base before setting the exponents equal to each other.

$(5^{-3})^{2\textit{x}-3} = 5^{-2}$

$\left(\frac{1}{125}\right)^{2\textit{x}-3} = \frac{1}{25}$

$-3(2\textit{x} - 3) = -2$

$\left(\frac{1}{5^3}\right)^{2\textit{x}-3} = \frac{1}{5^2}$

$-6\textit{x}+9 = -2$

$-6\textit{x} = -11$

$x=\frac{11}{6}$