molecular structure - How does VSEPR theory explain the formation of different bond angles in PCl₅?

We know, that in the exited state, electrons of Phosphorus could go to higher states and form $\ce{dsp^3}$ hybridization. Therefore it will create five equal energy states of electrons. But my question is that, why are the angles of the bonds in $\ce{PCl5}$ 90 and 120 degree instead of equally distributed? How does VSEPR theory explain the difference in the angles?

Why do the five equal bonding pairs of electrons have a trigonal bipyramidal arrangement, with two different internal bond angles - 120° in the plane and 90° between the plane and the axial atoms?