Identify the reason for existence of $PCl_5$ and non-existence of $NCl_5$

Nitrogen and phosphorus both belong to Group 15.

Their valence shell configurations are:

• Nitrogen: $2s^2 2p^3$
• Phosphorus: $3s^2 3p^3$

Bonding needed in $MCl_5$

In $MCl_5$, the central atom must accommodate five bonds.

• Phosphorus can form $PCl_5$ because it can expand its valence shell and achieve coordination number 5.
• Nitrogen, being a second-period element, has only $2s$ and $2p$ orbitals in its valence shell and cannot expand its octet.

Check each option

A: nitrogen is less reactive than phosphorus.
This is not the reason for non-existence of $NCl_5$. So, incorrect.

B: nitrogen doesn't have d-orbitals in its valence shell.
Nitrogen has no vacant $d$-orbitals in the second shell and cannot expand its octet, so $NCl_5$ is not formed. Correct.

C: catenation tendency is weaker in nitrogen than phosphorus.
Catenation is unrelated to formation of $NCl_5$. Incorrect.

D: size of phosphorus is larger than nitrogen.
Although phosphorus is larger, the key textbook reason is nitrogen's inability to expand octet. So incorrect.

Final answer

The correct option is: $\boxed{\text{B}}$

Comparison with stored correct answer

Stored correct answer: B
Derived answer: B
Hence, they agree.