Definition:T5 Space/Definition 2

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

$\left({S, \tau}\right)$ is a $T_5$ space iff each subset $Y$ contains a closed neighborhood of each $A \subseteq Y^\circ$ where $A^- \subseteq Y$.

In the above, $Y^\circ$ denotes the interior of $Y$ and $Y^-$ denotes the closure of $Y$.

Also see

 * Equivalent Definitions for $T_5$ Space