Answer
The lewis structures of both $NCl_3$ and $NCl_5$ are shown in the picture below. $NCl_5$ is not possible because of the excessive number of electrons around N.
Work Step by Step
$NCl_5$ is an unlikely structure because N is a second row element and cannot hold more than 8 electrons around it. $PCl_5$ is possible because P is a third row element and due to the d orbital it can hold more than 8 electrons around it.
