## \$h\$ is identity as soon as \$h(\Sigma)\cap \Sigma\$ contains at least 5 points

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 is there any papers proving this result?

Thank you very much