To solve the equation:

$\sqrt[3]{b} = -5$

we need to eliminate the cube root by raising both sides of the equation to the power of 3, as follows:

$(\sqrt[3]{b})^3 = (-5)^3$

This simplifies to:

$b = -125$

Thus, the solution is:

$b = -125$

Would you like more details or have any questions about this solution?

Here are five related questions that explore similar concepts:

1. How do we solve equations involving square roots with negative results?
2. What is the process for solving fourth-root equations?
3. Can all radical equations be solved by raising both sides to an exponent?
4. How do we verify solutions for radical equations?
5. What happens if the radical expression is in a fraction?

Tip: Always check your answer by substituting it back into the original equation, especially with radical equations, to ensure it satisfies the equation.