“Why do you think we “know” that?”
Because there are geometric principles that are mathematically and logically expressed in up to five dimensions.
A hypercube is mathematically true. Therefore even though we can’t directly observe it we know it is logical that it should exist and it is likewise irrational to argue that it can’t exist.
“Because there are geometric principles that are mathematically and logically expressed in up to five dimensions.”
The same principles can be expressed up to any arbitrary, or even an infinite number of dimensions, because they are simply mathematical abstractions, but that doesn’t tell us anything about the real world.
“A hypercube is mathematically true.”
Sure.
“Therefore even though we can’t directly observe it we know it is logical that it should exist...”
That’s called a non sequitur. Your conclusion does not follow from the argument you made. It’s logical that it COULD exist, not that it SHOULD exist.
“... and it is likewise irrational to argue that it can’t exist.”
I don’t think anyone argues that it “can’t” exist, but if you are doing science, you must demonstrate something exists, through experiment, rather than just positing that, since it might exist, we should assume it does.