Answer
$\frac{-1}{5x+2}$ (and $x\ne\frac{5}{2}$).
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
Hence here: $\frac{5x-2}{4-25x^2}=\frac{5x-2}{-((5x)^2-2^2)}=\frac{5x-2}{-(5x+2)(5x-2)}=\frac{-1}{5x+2}$ (and $x\ne\frac{5}{2}$).
