To simplify the expression ((3m - 7n)^2 - 9m(n - 5n)), we will follow these steps:

Calculate ((3m - 7n)^2):
[
(3m - 7n)^2 = (3m)^2 - 2 \cdot (3m)(7n) + (7n)^2
]
[
= 9m^2 - 42mn + 49n^2
]

Simplify (n - 5n):
[
n - 5n = -4n
]

Calculate (9m(n - 5n)):
[
9m(n - 5n) = 9m(-4n) = -36mn
]

Substitute back into the expression:
Now we put everything together:
[
(3m - 7n)^2 - 9m(n - 5n) = (9m^2 - 42mn + 49n^2) - (-36mn)
]

Combine like terms:
[
= 9m^2 - 42mn + 49n^2 + 36mn
]
[
= 9m^2 + (36mn - 42mn) + 49n^2
]
[
= 9m^2 - 6mn + 49n^2
]

Thus, the simplified expression is:
[
\boxed{9m^2 - 6mn + 49n^2}
]