solve an equation in complex plane $a(5-i)+b=ai-3$, $a$ and $b$ are conjugate complex number.
Find $a$ and $b$.
I have tried several methods to solve it but it stuck. 
How find the relationship of a and b in the equation with the complex number?

$a(5-i)+b=ai-3$
so
$b=a(2i-5)-3$
but 
$b=x+iy$
and
$a=x-iy$
$x+iy=(x-iy)(2i-5)-3=2ix-5x+2y+5iy-3=$
$=(2y-5x-3)+i(2x+5y)$
So you must solve the system 
$x=2y-5x-3$
and 
$y=2x+5y$
$x=\frac{y}{3}-\frac{1}{2}$
$y=\frac{2y}{3}-1+5y=\frac{17}{3}y-1$
To sum up 
$y=\frac{3}{14}$
$x=-\frac{3}{7}$
