Answer
$x^2=10y$
Work Step by Step
The general form of the equation of a parabola which opens upwards is
$x^{2}= 4py$
With the latus rectum intersecting the parabola when $x=5$
Thus, $|4p|=(2)(5)=10; p\gt 0$
Thus, the equation of the parabola becomes:
$x^{2}= 4py=(10)y$
$\implies x^2=10y$
