Prove that the integers $x$, $x+6$, $x+12$, $x+18$, $x+24$ can only be prime if $x$ is $5$.
I am very new to proofs and not completely sure of how to approach this one. I tried several different values for $x$ other than $5$ and came up with values that are not prime. However, I can't see how I could generalize this question to prove that it works if $x$ is $5$.
Help would be appreciated.