How to split $\frac{x^3}{(x^2+5)^2}$ into partial fractions? 
Split $\frac{x^3}{(x^2+5)^2}$ into partial fractions.

I have tried letting $$\frac{x^3}{(x^2+5)^2}=\frac{ax+b}{x^2+5}+\frac{cx^3+dx^2+ex+f}{(x^2+5)^2},$$ but this yields a system of only four simultaneous equations. 
I have also tried looking at $$\frac{x^3}{(x^2+5)^2} = x \cdot \left( \frac{x}{x^2+5} \right) ^2,$$ but sadly in vain.

Note that, by adding and subtracting $5x$ at the numerator, we obtain 
$$\frac{x^3}{(x^2+5)^2}=\frac{x^3+5x-5x}{(x^2+5)^2}=\frac{x(x^2+5)-5x}{(x^2+5)^2}=\frac{x}{x^2+5}-\frac{5x}{(x^2+5)^2}.$$
