Whether this is the "5th" dimension
or some other dimension, I couldn't really say. Nor could I say what this dimension would exactly relate to, but it's there in the math. It seems that way to me anyways, according to Science
's current take on Special Relativity
The Lorenz Transformation is a matrix transformation by which we translate one frame of reference to another, in Special Relativity. If you spend enough time playing with this transformation in 2D using one dimension to represent space and one to represent time, you start to realize that as one accelerates (ie. changes from one reference frame to another) the 2D graph looks like it is being rotated in 3D. So, 3D is nice and simple, we see 3D every day of our lives, it is easy to comprehend. This makes the whole nature of acceleration in special relativity much more intuitive.
It only gets really weird when you realize that that 3rd dimension isn't time, and it isn't a spatial dimension. It's something else. Why? The 2D graph we are drawing already accounts for time and space albeit in a dumbed-down 2D instead of 4D sense.
I took a course at NYU where among lots of other really well formatted material we were exposed to a number of lectures on Special Relativity. It was during some of the lessons about the Lorenz Transform that I noticed it looked like a 3D rotation and did a nice simple mock-up in Maya to show it. I asked the Proffessor after class and he told me he remembered something about a paper that claimed something similar. I could find only semi-relevant info about this on the web at the specialrelativity Yahoo Group.