Asymptotic optimality of the C5 construction

Prove that there exists an integer \(N_0\) such that \(\operatorname{rsat}(n,C_5)=2n-6\) for every \(n\ge N_0\).

Background

For $C_5$, the paper proves the upper bound $\operatorname{rsat}(n,C_5)\le 2n-6$ for sufficiently large $n$ and a lower bound that is weaker than $2n-6$. The authors state that they believe their constructions are optimal and formulate the eventual equality as a conjecture.