Higher dimensional geometry can show up in lower dimensional problems. This numberphile video (https://www.youtube.com/watch?v=6_yU9eJ0NxA) involves a puzzle about throwing darts at a dart board which is solved by using the volumes of 4+ dimensional spheres.

doesn't 4th just include time with a 3d object. Would things like waves/pulses fall under that? 5th seems to be used in the Kaluza-Klein theory[0] for gravitation and electromagnetism.

[0] https://en.m.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory

edit: I agree, I don't know why you got down voted. It was a thought provoking question.