Final answer:
Time does run slightly slower at the bottom of a tall building compared to the top due to gravitational time dilation, but the effect is so minuscule that it is not a reasonable excuse for being 5 minutes late to an appointment.
Step-by-step explanation:
The concept that your friend mentioned regarding time running faster at the top of a tall building actually has a basis in physics, specifically in Albert Einstein's theory of general relativity. In a very simplified explanation, the theory does predict that time would pass slightly slower the closer you are to a massive object due to the effects of gravity - a phenomenon known as gravitational time dilation. However, the difference is incredibly small and practically imperceptible in everyday life. For the Empire State Building, the difference would be fractions of a microsecond. So, although time does indeed run very, very slightly slower at the base compared to the top, this is not a reasonable excuse for your friend being 5 minutes late. Their lateness is more likely attributed to everyday delays such as traffic, slow elevators, or simply losing track of time.