The expression you provided is $\sqrt[3]{-125}$, which represents the cube root of $-125$.

To solve this, we can express $-125$ as:

$-125 = -5^3$

Since the cube root and the cube are inverse operations, the cube root of $-5^3$ is simply $-5$:

$\sqrt[3]{-125} = -5$

Thus, the value of $\sqrt[3]{-125}$ is $-5$.

Would you like further details or explanations on this?

Here are 5 related questions for further practice:

1. What is $\sqrt[3]{27}$?
2. How do you find $\sqrt[3]{-64}$?
3. Can cube roots of negative numbers always be real?
4. What is the cube root of $8$?
5. Simplify $\sqrt[3]{-8} + \sqrt[3]{64}$.

Tip: Cube roots of negative numbers are real because odd roots of negative numbers are negative.