KK-model (Kaluza-Klein) is a 5- dimensional model of the universe. It has been criticised of not having reality in all the dimensions. And there follows no evidence of the model.
In fact in the 4+1 model (4 space dimensions and 1 time dimension) the 4. dimension can be found in the reality. It is the fact that the space of the universe consists of all the space and there is no outside. Mathematically this simply is the 4. dimension of the space.
The evidence is that the going away of the galaxies, deduced of the red shift, happens in the 4- dimensional space, not in the 3- dimensional space. In this space happens like this and the expansion is not needed.
And other evidence is that we can keep on in the eternal and infinite (no border) space, which the space of universe rationally is.