I have a probability problem and I am given $P(X^2-12x+35>0)$ I know $X^2-12x+35>0$ can be factored into $(x-5)(x-7)>0$
The probabilities that it says I need are $P(x>7$ or $x<5)$
When I look at solving the inequality it looks like it should be $x>5$ and $x>7$
How do you get $x<5$
Your question has nothing to do with probability; it's really just about the inequality $(x-5)(x-7)\gt0$. In order for the product of two quantities, $x-5$ and $x-7$, to be positive, either each quantity is positive or each quantity is negative. (That is, the product of two negative numbers is positive.) If $x\gt7$, then each is positive; if $5\lt x\lt 7$, then $x-5$ is positive while $x-7$ is negative; and if $x\lt5$, then each is negative. That's why you get $(x-5)(x-7)\gt0$ if and only if $x\gt7$ or $x\lt5$.