1. The problem is to expand $(-5)^3$. 2. The expression $(-5)^3$ means multiplying $-5$ by itself three times. 3. The formula for powers is $a^n = a \times a \times \cdots \times a$ ($n$ times). 4. So, $(-5)^3 = (-5) \times (-5) \times (-5)$. 5. Calculate step by step: $$(-5) \times (-5) = 25$$ 6. Now multiply the result by $-5$: $$25 \times (-5) = -125$$ 7. Therefore, the expanded value of $(-5)^3$ is $-125$.