Explain why both N and Bi do not form pentahalides while phosphorus does.

Explanation

N does not form a pentahalide because it does not have d-orbitals to which 2s electron may be excited to make available five half-filled orbitals needed for the formation of five N-halogen bonds.
In contrast, Bi, in principle, can form a pentahalide because it has vacant 6d-orbitals to which 6s-electrons can be excited to make available five half filled orbitals needed for the formation of five Bi-halogen bonds.

But due to inert pair effect, the energy needed for excitation of 6s-electron to 6d-orbital is much more than the energy released when two additional Bi-halogen bonds are formed. Thus, bismuth does not form a pentahalide (except `BiF_(5)`) but forms only a trihalide.