In this article we obtain the rigid isotopy classification of generic rational curves of degre 5 in RP2\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {R}}{\mathbb {P}}^{2}$$\end{document}. In order to study the rigid isotopy classes of nodal rational curves of degree 5 in RP2\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {R}}{\mathbb {P}}^{2}$$\end{document}, we associate to every real rational nodal quintic curve with a marked real nodal point a nodal trigonal curve in the Hirzebruch surface Σ3\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma _3$$\end{document} and the corresponding nodal real dessin on CP1/(z↦z¯)\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {C}}{\mathbb {P}}^{1}/(z\mapsto {\bar{z}})$$\end{document}. The dessins are real versions, proposed by Orevkov (Annales de la Faculté des sciences de Toulouse 12(4):517–531, 2003), of Grothendieck’s dessins d’enfants. The dessins are graphs embedded in a topological surface and endowed with a certain additional structure. We study the combinatorial properties and decompositions of dessins corresponding to real nodal trigonal curves C⊂Σn\documentclass[12pt]{minimal}
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\begin{document}$$C\subset \Sigma _n$$\end{document} in real Hirzebruch surfaces Σn\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma _n$$\end{document}. Nodal dessins in the disk can be decomposed in blocks corresponding to cubic dessins in the disk D2\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf {D}}^2$$\end{document}, which produces a classification of these dessins. The classification of dessins under consideration leads to a rigid isotopy classification of real rational quintics in RP2\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {R}}{\mathbb {P}}^{2}$$\end{document}.
