I'll bet there are only four (length, width, height and time) but because someone screwed up a calculation early on, they've been adding "dimensions" to try to make it fit the original screwed up calculation.
(I have no proof, just an opinion. Let's just say that it wouldn't surprise me if it were so.)
Gah... this video has so many problems with it. The dimension of time is not like a spacial dimension, visualizing it as such causes problems. It shouldn't even really be called the "4th dimension"
Also, "flatlanders" should not be seeing two dimensions, they should be seeing one, which we can't even visualize. We in 3D world see two dimensions, only perceiving three with visual cues. And much of our perception of the 3D world consists of how 2D images change when we move or the world around us moves.