Simplify the given expression.

$25÷5\times 7\text{ of }(5+7)-13(6\times 4)$

The correct answer is 108.

To simplify the given numerical expression, we follow the BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction) rule for order of operations.

Given expression:

$25÷5\times 7\text{ of }(5+7)-13(6\times 4)$

Step 1: Simplify terms inside the brackets (Brackets first).

$5+7=12$

$6\times 4=24$

Substituting these values back into the expression gives:

$25÷5\times 7\text{ of }12-13\times 24$

Step 2: Evaluate the "Of" operation.
The "of" operation represents multiplication with higher priority than regular division and multiplication.

$7\text{ of }12=7\times 12=84$

Substituting this back into the expression:

$25÷5\times 84-13\times 24$

Step 3: Perform Division and Multiplication operations.

First, perform the division from left to right:

$25÷5=5$

Next, perform multiplication on the left part:

$5\times 84=420$

Then, perform multiplication on the right part:

$13\times 24=312$

The expression simplifies to:

$420-312$

Step 4: Perform Subtraction.

$420-312=108$

Thus, the final simplified answer is 108.