$\Big(\dfrac{-3}{5}\Big)^5$ is equal to :

1. $\dfrac{-243}{3125}$

2. $\dfrac{-81}{625}$

3. $\dfrac{81}{625}$

4. $\dfrac{512}{1875}$

If the base is negative and the exponent is odd, the result is negative.

$\Big(\dfrac{-3}{5}\Big)^5 \\[1em] = \dfrac{(-3)^5}{5^5} \\[1em] = \dfrac{(-3) \times (-3) \times (-3) \times (-3) \times (-3)}{5 \times 5 \times 5 \times 5 \times 5} \\[1em] = \dfrac{-243}{3125}$

Hence, option 1 is the correct option.