Peirce completed his work on graphical methods for reasoning within prepositional and predicate logic, but left unfinished similar systems for various modal logics. In the present paper, we put forward a system of Peircean graphs for reasoning within the modal logic S5. It is proved that our graph-based formulation of S5 is indeed equivalent to the traditional Hilbert-Frege formulation. Our choice of proof-rules for the system is proof-theoretically well motivated as the rules are graph-based analogues of Gentzen style rules as appropriate for S5. Compared to the system of Peircean graphs for S5 suggested in [17], our system has fewer rules (two instead of five), and moreover, the new rules seem more in line with the Peircean graph-rules for propositional logic.