Determine the elements of the set $\{ n \in \mathbb{N} :( \exists x,y \in \mathbb{N} )(n = 2x+3y) \}.$

Question

I let $n=1-9$ and solved for $x$ and $y$ to find the elements of the set. When $n=1-4$, you can't find an $x$ or $y$ to make the equality true. When $n=5$, it is true that $x=y=1$. But then, when $n=6$ you can't find two natural numbers that make it true. When $n$ is greater than or equal to $7$ though, you can find two natural numbers $x$ and $y$ to make it true. So I said my set was, $\{ n \in \mathbb{N}|n>6 \}$ but I think I have to include that $n=5$ as well as it is also true, but not quite sure how to include that. I have to prove this using induction but I've gotten stuck after multiple attempts. Any ideas would be helpful!