1. The problem asks for the volume of a sphere with radius $r=5$ cm. 2. The formula for the volume of a sphere is $$V=\frac{4}{3}\pi r^3$$ where $r$ is the radius. 3. Substitute $r=5$ into the formula: $$V=\frac{4}{3}\pi (5)^3$$ 4. Calculate the cube of 5: $$5^3=125$$ 5. So, $$V=\frac{4}{3}\pi \times 125$$ 6. Multiply numerator: $$V=\frac{500}{3}\pi$$ 7. To simplify, write intermediate step with cancellation: $$V=\cancel{\frac{500}{3}}\pi$$ (no common factors to cancel here, so just proceed) 8. Approximate $\pi \approx 3.1416$: $$V=\frac{500}{3} \times 3.1416 = 166.6667 \times 3.1416$$ 9. Multiply: $$V \approx 523.598$$ 10. Round to the nearest hundredth: $$V \approx 523.60$$ cm$^3$. Final answer: The volume of the sphere is approximately **523.60 cm$^3$**.