${\mathrm{PCl}}_5$ exists but ${\mathrm{NCl}}_{5 }$does not because : 

${\mathrm{PCl}}_5$​ forms five bonds by using the d-orbitals to "expand the octet" and have more places to put bonding pairs of electrons.${\mathrm{NCl}}_{5 }$​ does not exist because 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.