Determine which operation is needed in each so that the expression simplifies to 25 . Note: each operation $(+,-, X$, and $\div$ ) may be used more than once.
\[
40 \bigcirc 10 \bigcirc 4 \bigcirc(8 \bigcirc 2 \bigcirc 3) \bigcirc 5^{2}
\]

Step 1 ：First, we need to understand the problem. We are given an expression with five unknown operations, and we need to find the operations that will make the expression equal to 25.

Step 2 ：Let's start by simplifying the expression from left to right. We know that the operations are either addition, subtraction, multiplication, or division. We also know that the final result should be 25.

Step 3 ：We can start by trying different operations. Let's start with the first operation between 40 and 10. If we try addition, we get 50, which is already larger than 25. So, the first operation cannot be addition.

Step 4 ：If we try subtraction, we get 30, which is still larger than 25. So, the first operation cannot be subtraction.

Step 5 ：If we try multiplication, we get 400, which is much larger than 25. So, the first operation cannot be multiplication.

Step 6 ：If we try division, we get 4. This is less than 25, so it's possible that the first operation is division. Let's assume that the first operation is division for now.

Step 7 ：Next, we need to find the operation between the result of the first operation (4) and the next number (4). If we try addition, we get 8, which is less than 25. So, it's possible that the second operation is addition.

Step 8 ：If we try subtraction, we get 0, which is less than 25. However, no matter what operations we use for the remaining numbers, we cannot get 25 from 0. So, the second operation cannot be subtraction.

Step 9 ：If we try multiplication, we get 16, which is less than 25. So, it's possible that the second operation is multiplication.

Step 10 ：If we try division, we get 1, which is less than 25. However, no matter what operations we use for the remaining numbers, we cannot get 25 from 1. So, the second operation cannot be division.

Step 11 ：Next, we need to find the operation for the expression in the parentheses (8 \bigcirc 2 \bigcirc 3). If we try addition for both operations, we get 13, which is less than 25. So, it's possible that the operations in the parentheses are both addition.

Step 12 ：If we try subtraction for both operations, we get 3, which is less than 25. However, no matter what operations we use for the remaining numbers, we cannot get 25 from 3. So, the operations in the parentheses cannot be both subtraction.

Step 13 ：If we try multiplication for both operations, we get 48, which is larger than 25. So, the operations in the parentheses cannot be both multiplication.

Step 14 ：If we try division for both operations, we get 1.33, which is less than 25. However, no matter what operations we use for the remaining numbers, we cannot get 25 from 1.33. So, the operations in the parentheses cannot be both division.

Step 15 ：Next, we need to find the operation between the result of the second operation and the result of the operations in the parentheses. If we try addition, we get a number larger than 25. So, the third operation cannot be addition.

Step 16 ：If we try subtraction, we get a number less than 25. However, no matter what operations we use for the remaining numbers, we cannot get 25 from this number. So, the third operation cannot be subtraction.

Step 17 ：If we try multiplication, we get a number much larger than 25. So, the third operation cannot be multiplication.

Step 18 ：If we try division, we get a number less than 25. However, no matter what operations we use for the remaining numbers, we cannot get 25 from this number. So, the third operation cannot be division.

Step 19 ：Finally, we need to find the operation between the result of the third operation and the last number (5^{2}). If we try addition, we get a number larger than 25. So, the fourth operation cannot be addition.

Step 20 ：If we try subtraction, we get a number less than 25. However, no matter what operations we use for the remaining numbers, we cannot get 25 from this number. So, the fourth operation cannot be subtraction.

Step 21 ：If we try multiplication, we get a number much larger than 25. So, the fourth operation cannot be multiplication.

Step 22 ：If we try division, we get a number less than 25. However, no matter what operations we use for the remaining numbers, we cannot get 25 from this number. So, the fourth operation cannot be division.

Step 23 ：After trying all possible operations, we find that the operations that make the expression equal to 25 are: division for the first operation, multiplication for the second operation, addition for the operations in the parentheses, and subtraction for the third and fourth operations.

Step 24 ：So, the expression becomes: \(40 \div 10 \times 4 - (8 + 2 + 3) - 5^{2}\)

Step 25 ：Solving this expression, we get: \(4 \times 4 - 13 - 25 = 16 - 13 - 25 = 3 - 25 = -22\)

Step 26 ：However, -22 is not equal to 25. So, our assumption that the first operation is division, the second operation is multiplication, the operations in the parentheses are addition, and the third and fourth operations are subtraction is incorrect.

Step 27 ：Therefore, there is no combination of operations that can make the given expression equal to 25.