Simplify the given expression.

$\frac{13÷\{6-6÷(7-9)\times 8+9\}}{5+5\times 5÷\mathrm{5 }\text{of}\mathrm{ 5}}$

To simplify the given expression, we follow the order of operations rules (PEMDAS/BODMAS). Let's evaluate the numerator and the denominator separately.

The given expression is:
$\frac{13÷\{6-6÷(7-9)\times 8+9\}}{5+5\times 5÷5\text{of}5}$

Step 1: Simplify the Numerator
The numerator is: $13÷\{6-6÷(7-9)\times 8+9\}$
First, simplify the expression inside the innermost parentheses:
$7-9=-2$
Substitute this back into the numerator expression:
$13÷\{6-6÷(-2)\times 8+9\}$

Next, perform operations inside the curly braces. According to the order of operations, division and multiplication are performed from left to right:
1. Division: $6÷(-2)=-3$
The expression becomes: $6-(-3)\times 8+9$ which is $6+3\times 8+9$
2. Multiplication: $3\times 8=24$
The expression becomes: $6+24+9$
3. Addition: $6+24+9=39$

Now, substitute this simplified value back into the numerator:
Numerator = $13÷39=\frac{13}{39}=\frac{1}{3}$

Step 2: Simplify the Denominator
The denominator is: $5+5\times 5÷5\text{of}5$
According to BODMAS rules, the "of" operator has higher priority than division and multiplication, and is calculated as multiplication:
1. "of" operation: $5\text{of}5=5\times 5=25$
The denominator expression becomes: $5+5\times 5÷25$
2. Division: $5÷25=\frac{5}{25}=\frac{1}{5}$
The expression becomes: $5+5\times \frac{1}{5}$
3. Multiplication: $5\times \frac{1}{5}=1$
The expression becomes: $5+1$
4. Addition: $5+1=6$

So, the Denominator = 6.

Step 3: Combine Numerator and Denominator
Substituting the simplified values of the numerator and the denominator back into the main fraction:
$\text{Value}=\frac{\text{Numerator}}{\text{Denominator}}=\frac{1/3}{6}=\frac{1}{3\times 6}=\frac{1}{18}$

Therefore, the simplified value of the given expression is 1/18.