Factor the denominators.

$\frac{x-4}{\left(2x-1\right)\left(x+5\right)}+\frac{x+3}{x\left(x+5\right)}$

Multiply the fractions by a form of one to get a common denominator.

$\frac{x}{x}\left(\frac{x-4}{\left(2x-1\right)\left(x+5\right)}\right)+\left(\frac{x+3}{x\left(x+5\right)}\right)\frac{2x-1}{2x-1}$

$\frac{x^2-4x}{x\left(2x-1\right)\left(x+5\right)}+\frac{2x^2+6x-x-3}{x\left(2x-1\right)\left(x+5\right)}$

$\frac{3x^2+x-3}{2x^2+9x-5}$