Looking at the inequalities, we can see that the corresponding equations (y = -2x + 2 and y = -2x + 5) have the same slope, therefore they are parallel equations.
Since the solution for each inequality will be the region above the lines, so we need to choose the line that is above the other.
The y-intercept of the first one is 2, and the y-intercept of the second one is 5, therefore the line y = -2x + 5 is above the line y = -2x + 2.
That means the solution to this system will be:
Correct option: C.