D. No, the egg will not cook because the water temperature decreases as it boils.
The boiling point of water decreases as altitude increases, because the atmospheric pressure decreases. At an altitude of 5,300 meters, the boiling point of water is around 82°C. This means that the water will never reach the temperature of 100°C needed to cook a hard-boiled egg.
Even if the hiker leaves the egg in the boiling water for a longer time, the water temperature will not increase beyond 82°C, and the egg will not cook properly. Therefore, the hiker will not have hard-boiled eggs for breakfast.