1. **State the problem:** Simplify the expression $5a(a-3)-2a(a+4)$. 2. **Write the expression:** $5a(a-3)-2a(a+4)$. 3. **Apply the distributive property:** Multiply $5a$ by each term inside the first parentheses and $-2a$ by each term inside the second parentheses. $$5a \times a = 5a^2, \quad 5a \times (-3) = -15a$$ $$-2a \times a = -2a^2, \quad -2a \times 4 = -8a$$ 4. **Rewrite the expression with distributed terms:** $$5a^2 - 15a - 2a^2 - 8a$$ 5. **Combine like terms:** Group $a^2$ terms and $a$ terms. $$ (5a^2 - 2a^2) + (-15a - 8a)$$ 6. **Simplify each group:** $$ 5a^2 - 2a^2 = \cancel{5a^2} - \cancel{2a^2} = 3a^2$$ $$ -15a - 8a = -23a$$ 7. **Final simplified expression:** $$\boxed{3a^2 - 23a}$$