Identify the central atom and count the total number of electron groups (bonding and lone pairs) around it. For PF5, phosphorus (P) is the central atom bonded to five fluorine atoms, with no lone pairs on phosphorus.
Determine the electron geometry (eg) based on the total number of electron groups. Five bonding pairs correspond to a trigonal bipyramidal electron geometry.
Determine the molecular geometry (mg) by considering only the positions of the atoms (ignoring lone pairs). Since there are no lone pairs on phosphorus, the molecular geometry is the same as the electron geometry.
Recall that trigonal bipyramidal geometry has three atoms in an equatorial plane and two atoms in axial positions, which matches the structure of PF5.
Conclude that both the electron geometry and molecular geometry of PF5 are trigonal bipyramidal.