To solve the equation \( 5x^3 = -135 \), you would first use the operation of division by 5 to get the equation \( x^3 = -27 \). You would then use the inverse operation of \( x^3 \), which is taking the cube root of both sides. That leaves us one solution for \( x \).
The solution(s):
\[ x = \sqrt[3]{-27} = -3 \]
Thus, the solution is \( x = -3 \).