Sierpiński Space is T5

Theorem
Let $T = \left({\left\{{0, 1}\right\}, \tau_0}\right)$ be a Sierpiński space.

Then $T$ is a $T_5$ space.

Proof
The only closed sets in $T$ are $\varnothing, \left\{{1}\right\}$ and $\left\{{0, 1}\right\}$.

So there are no two separated sets $A, B \subseteq \left\{{0, 1}\right\}$.

So $T$ is a $T_5$ space vacuously.