Prove that every planar graph is the union of at most $5$ acyclic graphs.
Reminder: As union of two graphs $G_1(V_1, E_1)$ and $G_2(V_2, E_2)$ we consider the graph $G(V_1\cup V_2,E_1\cup E_2)$
I have tried induction on the number of vertices, but I seem to miss something