Step 1: Identify the geometry of PCl\(_5\).
PCl\(_5\) has trigonal bipyramidal geometry. Step 2: Axial and equatorial positions.
- 3 equatorial Cl atoms lie in one plane, separated by \(120^\circ\).
- 2 axial Cl atoms are perpendicular to the equatorial plane. Step 3: Bond angles.
Equatorial--equatorial angle = \(120^\circ\).
Axial--equatorial angle = \(90^\circ\). Step 4: Conclude.
Thus Cl--P--Cl angles are \(120^\circ\) and \(90^\circ\). Final Answer:
\[
\boxed{120^\circ \text{ and } 90^\circ}
\]