Question

Phosphorus form both PCl3 and PCl5 but nitrogen forms only NCl3 why?

Answer 1

N being member of second group cannot expand its octet so forms NCl3 only

Answer 2

Phosphorus has 15 electrons. So its electronic configuration is: $1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{3} 3d^{0}$
Phosphorus is a period 3 element. Hence it has an empty d-orbital which the period 2 elements do not have.
When phosphorus forms a compound, if there is enough energy available then one electron from one of the orbitals jumps to the vacant d-orbital. This gives phosphorus extra 2 valencies. This is called expanded octet.

As phosphorus initially has valency as 3 it forms PCl3, and due to this expanded octet, PCl5 can also be formed.
*Note that the expanded octet phenomenon can occur only in period 3 elements.

As Nitrogen lies in period 2, it does not have the empty d-orbital and so does not form NCl5