Answer
The equation's graph is symmetric only with respect to the $y$-axis.
Work Step by Step
We have $y=5x^2-1$.
(1) To test for symmetry about $x$-axis we replace $y$ by $-y$.
If the resulting equation is exactly the same as the original, then the function's graph is symmetric with respect to the $x$-axis.
$-y=5x^2-1$
This equation is not the same as the original hence there is no symmetry about the $x$-axis.
(2) To test the symmetry about y-axis we replace $x$ by $-x$.
If the resulting equation is exactly the same as the original, then the function's graph is symmetric with respect to the $y$-axis.
$y=5(-x)^2-1=5x^2-1$
This equation is the same as the original function hence there is symmetry about the $y$-axis.
(3) To test the symmetry about the origin we replace $x$ by $-x$ and $y$ by $-y$.
If the resulting equation is exactly the same as the original, then the function's graph is symmetric with respect to the origin.
$-y=5(-x)^2-1\\
-y=5x^2-1.$
This equation is not the same as the original hence there is no symmetry about the origin.
