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

First, we need to simplify the division of fractions:

2/3 - 5/7 ÷ 14/25
= 2/3 - 5/7 * 25/14
= 2/3 - 125/98

Next, we need to find a common denominator for the fractions:

2/3 = 2 * 98/3 * 98 = 196/294
125/98 = 125 * 3/98 * 3 = 375/294

Now we can subtract the fractions:

196/294 - 375/294 = -179/294

Therefore, the final answer is -179/294.