Question

Why ${PCl}_5$ exists but ${NCl}_5$ does not ?

Answer 1

$PC{l}_5$ forms five bonds by using the d-orbitals to "expand the octet" and have more "places" to put bonding pairs of electrons as it is an element of the 3rd period.

$NC{l}_5$ does not exist because it is an element of the 2nd period and there are no d-orbitals in the second energy level. Therefore there is no way to arrange five pairs of bonding electrons around a nitrogen atom.