When x=0, f(0) is the y intercept=0.
When f(x)=0, x=0, so both intercepts are zero.
There are asymptotes at x=±⁸√8. Also, when x is very large and positive, f(x)≃-5/x→0⁻ and when x is very large and negative, f(x)→0⁺.
f(x) is an odd function:
If x=c², f(c²)=-5c¹⁴/(c¹⁶-8), and f(-c²)=5c¹⁴/(c¹⁶-8). Therefore f(x)=-f(-x), which is asymmetrical. Symmetry is produced by double reflection in the axes (double flip): reflection in the y-axis then in the x-axis, or vice versa.