Evaluate the expression $21-\{8-5[6$ $4(8-7)-9(4-5)]-10+25 \times 2+13\}$.
$-36$
11
15
26

Step 1 ：First, we need to follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division, and Addition and Subtraction. We will start by solving the expressions inside the brackets and parentheses.

Step 2 ：Let's first solve the expressions inside the parentheses: \((8-7) = 1\) and \((4-5) = -1\)

Step 3 ：Now the expression becomes: \(21-\{8-5[6\ 4(1)-9(-1)]-10+25 \times 2+13\}\)

Step 4 ：Next, we will solve the expression inside the square brackets: \(6\ 4(1)-9(-1) = 6 \times 4 + 9 = 24 + 9 = 33\)

Step 5 ：Now the expression becomes: \(21-\{8-5[33]-10+25 \times 2+13\}\)

Step 6 ：Now, we will solve the expression inside the curly brackets: \(8-5[33]-10+25 \times 2+13 = 8 - 5 \times 33 - 10 + 25 \times 2 + 13\)

Step 7 ：Following the order of operations, we will perform multiplication first: \(8 - 165 - 10 + 50 + 13\)

Step 8 ：Now, we will perform addition and subtraction from left to right: \(-157 - 10 + 50 + 13 = -167 + 50 + 13 = -117 + 13 = -104\)

Step 9 ：Now the expression becomes: \(21 - (-104)\)

Step 10 ：Finally, we will perform the subtraction: \(21 - (-104) = 21 + 104 = 125\)

Step 11 ：Final Answer: \(\boxed{125}\)