Let $S_n$ be a symmetric group of $n$ elements acting on set by a natural map $$\pi : S_n \times[n] \mapsto [n]$$
As we know that there will be exactly one orbit because the action $\pi$ is transitive in this case. If we see the orbital graph it will be complete graph means every possible edge will be there in the graph.
Orbital graph : $G=(V,E)$, where $V=[n]$, $E = \{(i ,j) \in E, \exists \sigma , i^{\sigma} = j\}$.
Question : I want to find the non-trivial block which contain $5$. I don't know how to proceed further, please help.