Answer
$$y= \frac{1}{20}x^2 .$$
Work Step by Step
The vertex is at $(0,0)$ and the directrix is $y=-5=-c$; hence $c=5$. The parabola is vertical, opens upward, and has the equation
$$y=\frac{1}{4c}x^2=\frac{1}{20}x^2 .$$
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