$h$ 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