There's no reason why you can't talk about a 4th spatial dimension mathematically.
Yes, that's why I mentioned computer variable arrays - that is an example of a fourth "mathematical" dimension. You have x(a,b,c,d), where each index represents one "dimension" in the array. However, when talking about two-dimensional images and dimensions of our existence as we observe it, the first four dimensions are length, width, depth, and duration. While the images in this thread may be attempts at representing a mathematical system involving four spatial dimensions, our own universe contains only three spatial dimensions, so the images are "clipped" into the dimensions we perceive physically. We end up with a series of two-dimensional images, seen in a room represented in three, which itself moves through the fourth dimension of time.
The fifth dimension represents an infinite series of timelines - each one representing different events, perhaps different decisions we ourselves make (but certainly not limited to that). It is potentiality, possibility, probability, whatever you want to call it. Alternate "universes" which stem from our own universe's origin.