Explain why `PCl_(5)` is trigonal bipyramidal whereas `IF_(5)` is square pyramidal ?

Explanation

`PCl_(5)`- The ground state and the excited state outer electronic configurations of phosphorous (Z=15) are represented below.

In `PCl_(5)`, P is `sp^(3)d` hybridised, therefore, its shape is trigonal bipyramidal.
`IF_(5)`- The ground state and the exicted state outer electronic configuration of iodine (Z=53) are represented below.

In `IF_(5)`, I is `sp^(3)d^(2)` hybridised, therefore, shape of `IF_(5)` is square pyramidal.