In the paper "Normal Subgroups in the Cremona Group", under remark 5.1 they stated that for any generic set $\Sigma \subset \mathbb{P}^2_\mathbb{C}$ of $k$ points, and $h$ is an automorphism of $\mathbb{P}^2_\mathbb{C}$, then $h$ is the identity as soon $h(\Sigma)\cap \Sigma$ contains at least 5 points.

Can anyone be kind enough to show how do I prove it or are there any papers proving this result?

Thank you very much