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

First, let's simplify the expression (5/3)^-2:
(5/3)^-2 = (3/5)^2 = 9/25

Now, let's substitute back into the original expression:
(3 4/7) - 1 - 9/25

Next, convert the mixed number 3 4/7 to an improper fraction:
3 * 7 = 21
21 + 4 = 25
25/7 - 1 - 9/25

Now, let's find a common denominator for 7 and 25, which is 175:
175/7 - 175/25 - 63/25

Now, we can subtract the fractions:
175/7 = 25
175/25 = 7
25 - 7 - 63/25

Subtract 25 - 7:
25 - 7 = 18

Now we have:
18 - 63/25

To subtract fractions, we need to find a common denominator, which is 25:
18 * 25/25 - 63/25 = 450/25 - 63/25 = 387/25

Therefore, the final answer is: 387/25