Final answer:
The theory of general relativity indicates time dilation occurs but is minimal and not a reasonable excuse for 5-minute tardiness.
Step-by-step explanation:
The concept that time may run differently at various heights is related to Einstein's theory of general relativity, which suggests that time runs slightly slower the closer you are to a massive object due to the stronger gravitational field. However, this effect is so minute that it would not be noticeable over just a few minutes, like arriving 5 minutes late for a Valentine's Day meeting. While it's a creative excuse, unfortunately for your friend, time dilation on the scale of a tall building like the Empire State Building is not a reasonable excuse for being 5 minutes late.