The closest point shall be on the normal (perpendicular) to the line.
y = 2x - 4. slope of line is 2
]-1/2 is slope of normal
(y + 5) = -(x + 5) / 2
y + 5 = -x/2 + 2.5
y = -x/2 - 2.5, equation of normal
Now determine point of intersection of given line and normal. That is the closest point.