First things first. Solve the equation for y, getting it into y = mx + b form so it's easy to determine the slope. 5x + 2y = 12 so 2y = -5x + 12. Dividing everything by 2 we get 
. So the slope is -5/2. Parallel lines have the same slope, so we will have a slope of -5/2 in our new equation, we just have to find out what that equation is. We have an x and a y value from the point, so we will use that, along with the slope, to find b, the y-intercept. 
and 4 = 5 + b. So b = -1. Now let's write the equation: 
. And there you go!