[tex]\sin(x-y)=\sin x\cos y-\sin y\cos x[/tex]
Since [tex]\cos x=\dfrac8{17}[/tex], you have
[tex]\sin x=\sqrt{1-\cos^2x}=\sqrt{1-\left(\dfrac8{17}\right)^2}=\dfrac{15}{17}[/tex]
and since [tex]\cos y=\dfrac35[/tex], you have
[tex]\sin y=\sqrt{1-\cos^2y}=\sqrt{1-\left(\dfrac35\right)^2}=\dfrac45[/tex]
So,
[tex]\sin(x-y)=\dfrac{15}{17}\times\dfrac35-\dfrac45\times\dfrac8{17}=\dfrac{13}{85}[/tex]
Note that this assumes that both [tex]\sin x[/tex] and [tex]\sin y[/tex] are positive, or [tex]0<x<\pi[/tex].
