That in a picture with line graphs varying X, Y, people can't understand if the lines are different colours or the same colours (a third dimension)?
That people can't play 3D games because they can't understand that the image is depicting length, width and depth?
That people can't use windowing GUIs with overlapping windows, because they can't understand the Z-order of which window is "in front"?
It seems intuitive that people can cope with more than 2 variables and more than 2 "dimensions" spatially or otherwise.
What do you mean when you say they can't - what, specifically, can't people do?
Please note that I'm not saying it's impossible for people to intuitively understand 3 or more dimensions. Indeed as you say we do it every day. This is not the same as reasoning about it in a general way, which is much harder.
4 is pretty common too, but I agree that 4-5 is tricker to make sense of.