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:
 * every subset $Y \subseteq S$ contains a closed neighborhood of each $A \subseteq Y^\circ$ for which $A^- \subseteq Y$.

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

Also see

 * Equivalence of Definitions of $T_5$ Space