The conventional approach here would be to find the equation of the line. You can find the slope by subtracting the y coordinates of the two points, and then dividing by the difference in x coordinates:

m = (0 - 5)/(7 - 0) = -5/7

The y intercept of the line is 5, since (0,5) is on the line, so the equation of the line is

y = (-5/7)x + 5

If a point is on this line, then the equation above must be true if we plug in that point's coordinates. So we can now plug in each answer choice to see which works. If you plug in answer D (x = 14, y = -5), you get:

-5 = (-5/7)(14) + 5
-5 = -10 + 5
-5 = -5

so the equation is true, and D is on the line.

If you have a good conceptual understanding of slopes, you can bypass the calculations above. If a line travels from (0,5) to (7,0), it goes across 7 units and falls 5 units. So if we go across a further 7 units from the point (7,0), we must fall by a further 5 units. We'd then be at point (14,-5).
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Hey

The first thing I always do is trying to draw this as fast and accurate as possible.
When you draw the two points in a coordinate system, connect them with a line and extend the line, you clearly see what point could be on the line.
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