Show that the ideal of all polynomials of degree at least 5 in $\mathbb Q[x]$ is not prime 
Let $I$ be the subset of $\mathbb{Q}[x]$ that consists of all the
  polynomials whose first five terms are 0.

I've proven that $I$ is an ideal (any polynomial multiplied by a polynomial in $I$ must be at least degree 5), but I'm unsure to how to prove that it is not a prime ideal.  My intuition says that its not, because we can't use $(1)$ or $(x)$ as generators.  
I know that $I$ is a prime ideal $\iff$ $R/I$ is an integral domain.
Again, I'm a little confused on how represent $\mathbb{Q}[x]/I$    

Denote by $[f]$ the residue class of $f$ in $\Bbb{Q}[x]/I$. Then $[x],[x^4] \neq 0$, because neither $x \in I$ nor $x^4 \in I$. But what can you say about the product
$$
[x] \cdot [x^4]
$$
Can you conclude that $I$ is not a prime ideal?
