Answer
$(a)$ Symmetry with respect to $x$-axis
$(b)$ $x$-intercept $A(\sqrt5,0)$
$y$-intercept doesn't exist
Work Step by Step
$(a)$ As we can see from the image of the graph above, it is symmetrical with respect to the $x$-axis.
Algebraically, if we replace $y$ by $-y$ equation will be still equivalent to the original one.
$(b)$
$x$-intercept happens when $y=0$
$x^3+x\times 0^2=5$
$x^3=5$
$x=\sqrt{5}\approx 1.71$
$A(\sqrt5,0)$
$y$-intercept happens when $x=0$
$0^3+0\times y^2=5$
$y^2=\frac{5}{0}$
Such $y$ doesn't exist.
