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

Step 1: Simplify the fractions within the parentheses first
4/5 1 1/4 = 4/5 5/4 = 20/20 = 1

Step 2: Subtract the fractions within the parentheses
(23/25 - 13/15)
To subtract these fractions, we need to find a common denominator, which is 75. So we convert 23/25 to have a denominator of 75:
23/25 * 3/3 = 69/75

Now, we can subtract the fractions:
69/75 - 65/75 = 4/75

Step 3: Subtract the result from Step 2 from the result of Step 1
1 - 4/75 = 75/75 - 4/75 = 71/75

Step 4: Subtract 1/15 from the result
71/75 - 1/15
To subtract these fractions, we need a common denominator, which is 75:
71/75 - 5/75 = 66/75

Therefore, the final answer is 66/75.