To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, we need to simplify the division:

5/8 ÷ 35/24

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

5/8 × 24/35

Next, we multiply the numerators together and the denominators together:

(5 × 24) / (8 × 35)

120 / 280

Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 40:

120 ÷ 40 / 280 ÷ 40

3/7

Finally, we subtract 13 from 3/7:

13 - 3/7

To subtract fractions, we need a common denominator. The common denominator here is 7:

13/1 - 3/7

Now, we can subtract the fractions:

(13 × 7 - 3) / 7

(91 - 3) / 7

88/7

The final answer is 88/7.