Simplify the given expression:
$$25÷5\times 7\text{ of }(5+7)-13(6\times 4)$$

To solve this expression, apply the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction):
Given expression:

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

Step 1: Solve the brackets (B)

$$(5+7)=12$$

$$(6\times 4)=24$$

Substituting these values back into the expression:

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

Step 2: Solve 'Of' (O)

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

Now the expression becomes:

$$25÷5\times 84-13\times 24$$

Step 3: Solve Division (D)

$$25÷5=5$$

Now the expression becomes:

$$5\times 84-13\times 24$$

Step 4: Solve Multiplication (M)

$$5\times 84=420$$

$$13\times 24=312$$

Now the expression becomes:

$$420-312$$

Step 5: Solve Subtraction (S)

$$420-312=108$$