To solve the equation \( 5x^3 = -135 \), you would first use the division operation by dividing both sides 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 with one solution for \( x \). The solution is:
\[ x = \sqrt[3]{-27} = -3 \]
In summary, the solution(s): \( x = -3 \).