  In this paper, we study the flexibility of two planar graph classes
$\mathcal{H}_1$, $\mathcal{H}_2$, where $\mathcal{H}_1$, $\mathcal{H}_2$ denote
the set of all hopper-free planar graphs and house-free planar graphs,
respectively. Let $G$ be a planar graph with a list assignment $L$. Suppose a
preferred color is given for some of the vertices. We prove that if $G\in
\mathcal{H}_1$ or $G\in \mathcal{H}_2$ such that all lists have size at least
$5$, then there exists an $L$-coloring respecting at least a constant fraction
of the preferences.
