Answer
$y^2=20 x$
Work Step by Step
We are given that the vertex is at origin, that is, $(0,0)$. and the focus is at $(5,0)$.
The fact that the focus is at $(p,0)=(5,0)$ implies that the parabola is horizontal and $p=5$.
The general form of a horizontal parabola is $y^2=4px$ when the vertex is at origin.
Thus, the general form of a horizontal parabola becomes:
$$y^2=(4)(5)x \\
\implies y^2=20 x$$
