A light ray coming along the line $3x+4y=5$ gets reflected from the line  $ax+by=1$ and goes along the line $5x-2y=10$. Then, 

 $ax+by=1$ will be one of the bisectors of the given line. Equation of bisectors of the given lines are $\frac{3x+4y-5}{5}=\pm \left(\frac{5x-12y-10}{13}\right)$ 

$\Rightarrow$ $64x-8y=115$ or $14x+112y=15$

$\Rightarrow$$a=\frac{64}{115}, b-\frac{8}{115}$ or $a=\frac{14}{15}, b=\frac{12}{115}$