We use

sin(α − β) = sin α cos β − cos α sin β

We firstly need to find cos α and sin β.

If sin α = 4/5, then we can draw a triangle and find the value of the unknown side using Pythagoras' Theorem (in this case, 3):

We do the same thing for cos β = 12/13, and we obtain the following triangle. We have used Pythagoras' Theorem to find the unknown side.

Now for the unknow ratios in the question:

cos α = 3/5

(positive because in quadrant I)

sin β = 5/13

(positive because in quadrant II)

We are now ready to find the required value, sin(α − β):

This is the exact value for sin(α − β).