Four dimensions is easy. Meet me on the 5th floor at Main Street and Second Avenue at 3 pm today and I'll tell you all about it.
Five dimensions (of which the ARTICLE speaks) is beyond me! I seem to recall a high-school report where I had a duplicated a drawing that somehow represented the numerous (27??) dimensions that Einstein somehow figured there are???!!
There are an infinite number of possible solutions to Einstein's equations, and an infinite number of them are also physically possible in our universe as we know it. A five-dimensional solution was one of the first proposed to Einstein, and it is a solution, but Einstein rejected it because it did not pass the reality test.
Five dimensions = alternate realities.