Answer
(a) Focus: $F(0,\frac{5}{4})$
Directrix: $y=-\frac{5}{4}$
$Focal~diameter=5$
(b)
Work Step by Step
Equation of a parabola with vertical axis: $x^2=4py$
$x^2=5y$
$4p=5$
$p=\frac{5}{4}$
Focus: $F(0,p)=F(0,\frac{5}{4})$
Directrix: $y=-p=-\frac{5}{4}$
$Focal~diameter=|4p|=5$