Prove by contradiction that any prime number is either in the from of $ab+1$ or $ab+5$. It says:

Prove by contradiction that any prime number is either of the form of $ab+1$ or $ab+5$.

And this was all. But it seems both belong to $\mathbb{N} \cup \{0\}$. Because otherwise it wouldn't hold for $2$ which is prime.
What the problem says is to say:
$$(p\neq ab+1)\wedge (p\neq ab+5)\implies p\text{ is not prime}$$
I tried to show it would then be written as the product of two numbers and thus not prime. But up to what number should I do that?
Stuck.

HINT: Consider modulus 6. A number $p $ taken modulus 6 can only be $0, 1, 2, 3, 4$ or $5$. What happens if $p $ is either $0, 2$ or $4$ mod 6? What if it is $3$ mod 6?
