Why are axial bonds of $ PC{{l}_{5}} $ longer than equatorial bonds ?

Hint: The chemical compound $ PC{{l}_{5}} $ stands for phosphorus pentachloride. One of the most important phosphorus chlorides, along with $ PC{{l}_{3}} $ and $ POC{{l}_{3}} $ . As a chlorinating reagent, $ PC{{l}_{5}} $ is used. Although commercial samples can be yellowish and polluted with hydrogen chloride, it is a colourless, water-sensitive, and moisture-sensitive solid.

Complete answer:
Depending on the bond angle, non-ring atom bonds are referred to as axial or equatorial. Axially bonded non-ring atoms at angles of roughly $ {{90}^{o}} $ degrees to the ring plane are referred to as axial bonds. Equatorial bonds are those with non-ring atoms that make just a tiny angle with the ring plane.
Hybridization of phosphorus is $ s{{p}^{3}}d $ . It creates 5 $ s{{p}^{3}}d $ orbitals that are comparable. There is one unpaired electron in each of them. $ PC{{l}_{5}} $ has a trigonal bipyramidal structure, with three chlorine atoms at the triangle's corners and two chlorine atoms axially located. Axial bond length is longer than equatorial bond length to minimise bond pair – bond pair repulsion between axial and equatorial bonds.
This is due to the equatorial bond pairs of electrons repelling the axial bond pairs more strongly.
Three equatorial bonds and two axial bonds exist in $ PC{{l}_{5}} $ . Because of the stronger repulsion from equatorial bonds, axial bonds are longer than equatorial bonds. As axial bonds approach equatorial bonds, increased repulsion occurs, resulting in bond length elongation. The $ PC{{l}_{5}} $ molecule has a trigonal bipyramidal shape. $ {{90}^{o}} $ and $ {{120}^{o}} $ degrees are the bond angles. The five $ s{{p}^{3}}d $ hybrid orbitals are all filled by a single atom. Five sigma bonds are formed when these hybrid orbitals collide with a singly filled $ 3{{p}_{z}} $ atomic orbital of five Chlorine atoms (P- Cl).

Note:
The chlorination of $ PC{{l}_{3}} $ produces $ PC{{l}_{5}} $ . Around 10,000 tonnes of $ PC{{l}_{5}} $ are produced every year using this reaction. Because $ PC{{l}_{5}} $ reacts aggressively with water, it is a toxic chemical. When it comes into touch with skin, it's corrosive, and inhaling it can be lethal.