  In this article we obtain the rigid isotopy classification of generic
rational curves of degre $5$ in $\mathbb{R}\mathbb{P}^{2}$. In order to study
the rigid isotopy classes of nodal rational curves of degree $5$ in
$\mathbb{R}\mathbb{P}^{2}$, we associate to every real rational nodal quintic
curve with a marked real nodal point a nodal trigonal curve in the Hirzebruch
surface $\Sigma_3$ and the corresponding nodal real dessin on
$\mathbb{C}\mathbb{P}^{1}/(z\mapsto\bar{z})$. The dessins are real versions,
proposed by S. Orevkov, 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 $C\subset \Sigma_n$ in real
Hirzebruch surfaces $\Sigma_n$. Nodal dessins in the disk can be decomposed in
blocks corresponding to cubic dessins in the disk $\mathbf{D}^2$, which
produces a classification of these dessins. The classification of dessins under
consideration leads to a rigid isotopy classification of real rational quintics
in $\mathbb{R}\mathbb{P}^{2}$.
