1. **State the problem:** We are given two functions $f(x) = 5 - x^3$ and $g(x) = x^2$. We need to find the derivative of the composition $(f \circ g)'(x)$, which means the derivative of $f(g(x))$. 2. **Recall the chain rule:** The derivative of a composition of functions is given by: $$ (f \circ g)'(x) = f'(g(x)) \cdot g'(x) $$ This means we first find the derivative of $f$ evaluated at $g(x)$, then multiply by the derivative of $g$. 3. **Find $f'(x)$:** Given $f(x) = 5 - x^3$, differentiate term-by-term: $$ f'(x) = 0 - 3x^2 = -3x^2 $$ 4. **Find $g'(x)$:** Given $g(x) = x^2$, differentiate: $$ g'(x) = 2x $$ 5. **Apply the chain rule:** Substitute $g(x) = x^2$ into $f'(x)$: $$ f'(g(x)) = f'(x^2) = -3(x^2)^2 = -3x^4 $$ 6. **Multiply by $g'(x)$:** $$ (f \circ g)'(x) = f'(g(x)) \cdot g'(x) = (-3x^4)(2x) = -6x^5 $$ **Final answer:** $$ (f \circ g)'(x) = -6x^5 $$