Answer
Please see the graph.
Vertex: $(0, 5)$
x-intercepts: -1, 1
y-intercepts: 5
Work Step by Step
$f(x)=-5x^2+5$
$a=-5$, $b=0$, $c=5$
$x=-b/2a$ is the vertex.
$x=-b/2a$
$x=-0/2*-5$
$x=-0/-10$
$x=0$
$f(x)=-5x^2+5$
$f(0)=-5*0^2+5$
$f(0)=-5*0+5$
$f(0)=0+5$
$f(0)=5$
$y=0$
$f(x)=-5x^2+5$
$0=-5x^2+5$
$0=-5(x^2-1)$
$0/-5=-5(x^2-1)/-5$
$0=x^2-1$
$0=(x+1)(x-1)$
$x+1=0$
$x+1-1=0-1$
$x=-1$
$x-1=0$
$x-1+1=0+1$
$x=1$
