Let $\pi: X\rightarrow \mathbb{P_\mathbb{R}^1}$ be a conic bundle ($\mathbb{R}$-minimal) with 3 reducible fibres. Consider $X$ as $G$-surface where $G\subset Aut_\mathbb{R}(X)$ is a group of order $5$. Hence $G$ acts on $\mathbb{P_\mathbb{R}^1}$.

How can I see that $G$ has at least $3$ fixed points on $\mathbb{P_\mathbb{R}^1}$?