1. **State the problem:** Simplify or expand the expression $x^3(y - 5)(x - 8)$. 2. **Recall the distributive property:** To expand, multiply each term in one parenthesis by each term in the other. 3. **First, expand $(y - 5)(x - 8)$:** $$ (y - 5)(x - 8) = y \cdot x - y \cdot 8 - 5 \cdot x + 5 \cdot 8 = xy - 8y - 5x + 40 $$ 4. **Now multiply the result by $x^3$:** $$ x^3(xy - 8y - 5x + 40) = x^3 \cdot xy - x^3 \cdot 8y - x^3 \cdot 5x + x^3 \cdot 40 $$ 5. **Simplify each term:** $$ x^3 \cdot xy = x^{3+1}y = x^4 y $$ $$ x^3 \cdot 8y = 8x^3 y $$ $$ x^3 \cdot 5x = 5x^{3+1} = 5x^4 $$ $$ x^3 \cdot 40 = 40x^3 $$ 6. **Write the fully expanded expression:** $$ x^4 y - 8x^3 y - 5x^4 + 40x^3 $$ 7. **Final answer:** $$ \boxed{x^4 y - 8x^3 y - 5x^4 + 40x^3} $$