1. We are given the inequality $5 > 3$ and asked to multiply both sides by $-3$ and then compare the results. 2. Multiplying both sides by $-3$, we get: $$5 \times (-3) \quad \text{and} \quad 3 \times (-3)$$ 3. Since multiplying an inequality by a negative number reverses the inequality sign, we have: $$5 > 3 \implies 5 \times (-3) < 3 \times (-3)$$ 4. Calculating the products: $$5 \times (-3) = -15$$ $$3 \times (-3) = -9$$ 5. So the inequality becomes: $$-15 < -9$$ 6. Therefore, the correct answer is option c: $-15 < -9$.