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.

The gauge group of the Standard Model, i.e., including electroweak and strong interactions, is SU(3) X SU(2) X U(1) (modulo some technicalities that I don't think matter for this discussion). This is a six-dimensional group, so you need six compactified dimensions in addition to the four dimensions of spacetime that we know in order to construct a Kaluza-Klein/string theory type model that includes all the Standard Model interactions. AFAIK the Calabi-Yau manifolds that are talked about in string theory are examples of six-dimensional compactified spaces that can be used in such a model.

A similar problem occurred in the formation of drops and bubbles where at those tiny scales right before it pinches off molecular effects come in to play.

However, through a mathematical method, scientists were able to ignore those molecular effects.

Black strings are entirely hypothetical. Scientists are hoping they can be pinched off in the same way as bubbles and that, if they can, they can use the same method above to ignore quantum effects (in the way molecular effects are ignored in bubbles). If so, it could (theoretically) be applied to the study of black holes, allowing scientists to study black holes without a quantum theory of gravity.