The fifth dimension is theoretical, yes. It turns out that you can get classical electricity and magnetism out of the Einstein equations by adding a fifth, rotationally symmetric spatial dimension (https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory). Some people had hopes that quantum mechanics could fall out of the einstein equations in a similar fashion and this hope sort of lead to string theory, which needs to add further dimensions beyond the rotationally symmetric U(1) group of Kaluza-Klein theory to support the SO(3) (I believe) group of the electro-weak force (so they add 4 more dimensions) then further dimensions for the strong force symmetries. This latter part isn't my specialty so I am hazy on the details, but it falls under gauge theory.

So, while the fifth dimension is at the moment largely theoretical, it holds some interest in the field of gravitational physics due to some elegant constructions that fall out of it. It may be that the scalar field it predicts could describe dark matter: https://arxiv.org/abs/hep-ph/0207125.