To solve this expression, we need to perform the division and subtraction operations in order.

First, divide -8/15 by 13/16:
(-8/15) ÷ (13/16) = (-8/15) * (16/13) = -128/195

Next, subtract 13/30 from the result:
(-128/195) - (13/30) = (-128/195) * (30/30) - (13/30) = (-3840/5850) - (13/30) = (-3840/5850) - (507/1170)

To simplify further, we need to find a common denominator for the fractions. The least common multiple of 5850 and 1170 is 5850.

(-3840/5850) - (507/1170) = (-3840/5850) * (2/2) - (507/1170) = (-7680/11700) - (507/1170)

Now, we can subtract the fractions:
(-7680/11700) - (507/1170) = (-7680 - (507 * 10))/(11700) = (-7680 - 5070)/11700 = -12750/11700

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 150:
-12750/11700 = (-12750 ÷ 150)/(11700 ÷ 150) = -85/78

Therefore, the simplified value of the expression -8/15 ÷ 13/16 - 13/30 is -85/78.