Hint: Have you tried proving this by induction on $V$?
The objective is to prove $P(n) = $ "Any planar graph $G$ with $V \geq 2$ vertices, there exist two vertices of degree $\leq 5$." (You need to show that two distinct such vertices exist, and that will suffice.)
$(1)$ Start with base-case: Show that for $G$ with $V = 2$ vertices, each vertex has degree 2. (That is, $P(2)$ is trivially true).
$(2)$ Assume $P(k)$ is true when $V = k$.
$(3)$ Then, show that if one more vertex is added to $G$, so $G$ has $V = k + 1$ vertices, it follows from $P(k)$ that $P(k+1)$ is also true.
Then you will have shown that $P(n)$ is true.