Why spacetime has 3+1 large dimensions and remaining higher dimensions underwent compactification? Why spacetime hasn't got eg. 5+4 or 3+5 dimensions?

Yesterday I wrote very, very big thread which proved to be too broad, so according to your instructions I divided it. Content is unchanged.

I read that it might be related to the phenomenon of spontaneous symmetry breaking. After Big Bang, universe underwent spontaneous symmetry breaking, in which ten dimensions randomly divided into four dimensional and six dimensional parts. Four of them underwent inflation to macroscopic scale, while the other six had been compactified. This theory makes sense to me but I'm not sure if it is appropriate.