I am predisposed to be skeptical of versions of fundamental theories of physics that require more than the common place three dimensions of space and one dimension of time that are commonly observed (although theories like loop quantum gravity in which the four common dimensions are emergent properties of a more fundamental theory can be tolerable).
Never the less, a 2003 speculative physics paper by Paul S. Wesson illustrates in a way just barely comprehensible by a sophisticated layman, the beauty possible in a 5-D theory that drives many of the world's top theoretical physics egg heads to consider it seriously.
The wonder of Wesson's paper is that it uses the proposed 5th dimension to turn concepts like Heisenberg's uncertainty principle and quantum randomness, into a property of a larger deterministic (i.e. non-random) theory, and it also suggests how apparent non-local or non-causal action in quantum physics can actually be causal and local in a 5th dimension. In short, it can make quantum physics much less weird.
It isn't that I agree that Wesson's version of a 5-D theory is correct. Indeed, the tone of the paper strongly suggests that he also, while believing he is on the right track, doesn't think his theory is correct either. But, a physics that uses one odd assumption to resolve many other head scratchers is attractive, in much the same way that general relativity has (appropriately and based upon empirical evidence) won over all mainstream physicists with the same sort of gambit.