Two quick thoughts on the philosophical nature of this. (And ignoring the mathematics. )

1. I was always intrigued by super symmetry, the mathematical correctness that occurs if we assume there are something like 11 dimensions? Pretty much dismissed these days, but...

2. One thing we know from observation is that a dimension allows access to other parts of a previous dimension. When you raise a pen off of a piece of paper and write another letter in another space, you have used the third dimension to traverse the other two. Time allows us to traverse our three dimensional world. What would a fifth dimension allow?