You have to find cos(x) from sin(x) =4/5, which would be:cos(x) =3/5. Then;

You have to find cos(y) from sin(y) =5/13, which would be:cos(y) =12/13. Then:

You have to use this formula: sin(x + y) = sin x cos y + cos x sin y=4/5*12/13 + 3/5*5/13 =**63/65 **