Find the point on the line y=5x+4 that is closest to the origin

That point will be on the perpendicular line through the origin,
  y = (-1/5)x
so will satisfy
  (-1/5)x = 5x +4
  (-26/5)x = 4
  x = 4*(-5/26) = -10/13
  y = (-1/5)x = 2/13

The point of interest is (-10/13, 2/13)