Rewrite $\left(\frac{-3}{5}\right)^{5}$ as $\left(\frac{-3}{5}\right)^{3}\times \left(\frac{-3}{5}\right)^{2}$. Cancel out $\left(\frac{-3}{5}\right)^{3}$ in both numerator and denominator.
$$\frac{1}{\left(\frac{-3}{5}\right)^{2}}$$
Fraction $\frac{-3}{5}$ can be rewritten as $-\frac{3}{5}$ by extracting the negative sign.
$$\frac{1}{\left(-\frac{3}{5}\right)^{2}}$$
Calculate $-\frac{3}{5}$ to the power of $2$ and get $\frac{9}{25}$.
$$\frac{1}{\frac{9}{25}}$$
Divide $1$ by $\frac{9}{25}$ by multiplying $1$ by the reciprocal of $\frac{9}{25}$.
$$1\times \frac{25}{9}$$
Multiply $1$ and $\frac{25}{9}$ to get $\frac{25}{9}$.
