The geometry of a molecule refers to the arrangement of atoms in three-dimensional space. In the case of PCl5 (phosphorus pentachloride), the molecule adopts a trigonal bipyramidal geometry. Let's break down the reasons behind this answer:

- Phosphorus Atom: The central atom in PCl5 is phosphorus (P). Phosphorus belongs to Group 5A of the periodic table and has five valence electrons.

- Chlorine Atoms: There are five chlorine (Cl) atoms bonded to the central phosphorus atom. Chlorine belongs to Group 7A and has seven valence electrons.

- Bonding: Phosphorus forms single bonds with each of the five chlorine atoms, resulting in a total of five P-Cl bonds. Each chlorine atom contributes one electron to form a covalent bond with phosphorus.

- Lone Pairs: After forming the P-Cl bonds, the phosphorus atom has three lone pairs of electrons. These lone pairs are not involved in bonding and are located in the valence shell of the phosphorus atom.

- Electron Pair Repulsion Theory: The geometry of a molecule is determined by the electron pair repulsion theory. According to this theory, electron pairs (both bonding and lone pairs) repel each other and try to maximize their separation to minimize repulsion.

- Trigonal Bipyramidal Geometry: In the case of PCl5, the five bonding pairs and three lone pairs of electrons around the phosphorus atom repel each other. To minimize repulsion, the electron pairs arrange themselves in a trigonal bipyramidal geometry.

- Trigonal Planar Equatorial Plane: Three of the bonding pairs and one of the lone pairs occupy the equatorial positions in a trigonal plane. This gives the molecule a trigonal planar shape in the equatorial plane.

- Axial Position: The remaining two bonding pairs and two lone pairs are located in the axial positions, perpendicular to the trigonal plane. This gives the molecule a bipyramidal shape.

- Overall Shape: The combination of the trigonal planar equatorial plane and the axial positions results in a trigonal bipyramidal geometry for the PCl5 molecule.

In conclusion, the PCl5 molecule adopts a trigonal bipyramidal geometry due to the arrangement of its bonding and lone pairs of electrons around the central phosphorus atom.