One could waste one's entire life trying to correct rubbish attempts at physics on the internet, especially when it's full of non-sequiturs like the video. But as a start, the description of quantum mechanics is nonsense and I'm guessing the narrator got their understanding of it by reading popsci books (I'm trying to avoid a personal attack on the author, but it's hard when they've said a lot of wrong things so very confidently). The dimensionality of a typical QM Hilbert space is infinite, not five. People get wound up wondering what the N^th dimension is, when all dimensionality is, somewhat simplified, is how many numbers you need to describe the position of something.
The top comment on this stack exchange thread has more: http://physics.stackexchange.com/questions/55824/is-imaginin...