In the paper ["Normal Subgroups in the Cremona Group"][1], 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


  [1]: https://link.springer.com/content/pdf/10.1007/s11511-013-0090-1.pdf