sin(u - v) = sin(u)*cos(v) - sin(v)*cos(u).

We know sin(u) and cos(v) so have to find cos(u) and sin(v).

cos(u) = +-sqrt[1-(sin(u))^2] = +-sqrt(144/169) = +-(12/13). Choose "+" sign because 0<u<pi/2.

sin(v) = +-sqrt[1-(cos(v))^2] = +-sqrt(16/25) = +-(4/5). Choose "+", sin(v)>=0 when pi/2<v<pi.

Gathering all we obtain

sin(u-v) = (5/13)*(-3/5) - (4/5)*(12/13) = -(1/(5*13))*(15 + 48) = -63/65.

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