Final answer:
While time runs slightly faster at the top of a high building due to relativity, the difference is incredibly small and would not be noticeable in everyday life, making your friend's excuse scientifically inaccurate for practical purposes.
Step-by-step explanation:
The concept being discussed here involves principles of physics, and specifically relates to the theory of relativity. According to the theory of relativity, time dilation occurs due to differences in gravity as per Einstein's equations. Thus, theoretically, time does indeed run slightly faster at the top of a high building than at its base due to a weaker gravitational pull. However, for practical purposes, like meeting someone at the Empire State Building, this difference is incredibly minute and would not account for a 5-minute delay. Therefore, your friend's excuse that time runs faster at the top of the building is not valid for everyday experiences and timekeeping. In real-life scenarios, standard clocks and watches are not affected by such infinitesimal differences in time dilation caused by gravity at different altitudes.