${\mathrm{PCl}}_5$ Exists but ${\mathrm{NCl}}_5$ Does Not Why?

${\mathrm{PCl}}_5$ exists but ${\mathrm{NCl}}_5$ does not:

• Phosphorous belongs to the second period of the periodic table, hence it does have vacant d orbitals which it can use to expand its octet during bond formation.
• Hence, in the formation of $\mathrm{PC}{\mathrm{l}}_5$, Phosphorous uses its five d-orbitals by expanding its the octet to form five bonds with the five respective Chlorine atoms.
• However, the nitrogen belongs to the first period, having no vacant d orbitals to expand further for bond formation
• Thus, the molecule ,$\mathrm{NC}{\mathrm{l}}_5$ does not exist as there are no d-orbitals available in the Nitrogen valence shell, for which there is no way to arrange five pairs of bonding electrons around a nitrogen atom, and formation of five bonds with the five Chlorine atoms.

Hence, the reason why ${\mathrm{PCl}}_5$ exists but ${\mathrm{NCl}}_5$ does not, has been explained above.