Identify the central atom in the molecule, which is phosphorus (P) in PCl5.
Determine the number of valence electrons for the central atom. Phosphorus has 5 valence electrons.
Count the number of atoms bonded to the central atom. In PCl5, there are 5 chlorine atoms bonded to phosphorus.
Use the VSEPR (Valence Shell Electron Pair Repulsion) theory to predict the electron geometry. Since there are 5 bonding pairs and no lone pairs on phosphorus, the electron pairs will arrange themselves to minimize repulsion.
Recognize that 5 bonding pairs around the central atom correspond to a trigonal bipyramidal electron geometry.