A spherical exoplanet is orbited by a small scientific probe in a circular orbit just above the planet's surface at an altitude that is negligible compared to the planet's radius. The orbital period of the probe is measured to be \(T = 5.0 \times 10^3 \text{ s}\). Assuming the planet has a uniform mass distribution and using the universal gravitational constant \(G = 6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2/\text{kg}^2\), what is the average mass density of the planet?