1. **State the problem:** We are given the polynomial function $p(a) = a^3 - 5$ and asked to find $p(x - 4)$. 2. **Formula used:** To find $p(x - 4)$, substitute $a$ with $(x - 4)$ in the function $p(a)$. 3. **Substitution:** $$p(x - 4) = (x - 4)^3 - 5$$ 4. **Expand the cube:** Recall the binomial expansion formula: $$(x - 4)^3 = x^3 - 3 \cdot x^2 \cdot 4 + 3 \cdot x \cdot 4^2 - 4^3$$ 5. **Calculate each term:** $$x^3 - 12x^2 + 48x - 64$$ 6. **Substitute back:** $$p(x - 4) = x^3 - 12x^2 + 48x - 64 - 5$$ 7. **Simplify:** $$p(x - 4) = x^3 - 12x^2 + 48x - 69$$ **Final answer:** $$p(x - 4) = x^3 - 12x^2 + 48x - 69$$