`{:("A B"),("x 5"),(---),("C A B"),(---):}`

Answer

To solve the problem where \( AB \times 5 = CAB \), we will break it down step by step.

### Step 1: Understand the notation
The notation \( AB \) represents a two-digit number where \( A \) is the tens digit and \( B \) is the units digit. Therefore, we can express \( AB \) as:
\[ AB = 10A + B \]

### Step 2: Set up the equation
Given the equation \( AB \times 5 = CAB \), we can substitute \( AB \) into the equation:
\[ (10A + B) \times 5 = CAB \]
The number \( CAB \) can be expressed as:
\[ CAB = 100C + 10A + B \]
Thus, we can rewrite our equation as:
\[ 5(10A + B) = 100C + 10A + B \]

### Step 3: Expand and simplify
Expanding the left side gives us:
\[ 50A + 5B = 100C + 10A + B \]
Now, we will move all terms to one side:
\[ 50A + 5B - 10A - B = 100C \]
This simplifies to:
\[ 40A + 4B = 100C \]

### Step 4: Factor the equation
We can factor out 4 from the left side:
\[ 4(10A + B) = 100C \]
Dividing both sides by 4 gives:
\[ 10A + B = 25C \]

### Step 5: Analyze the equation
From \( 10A + B = 25C \), we know that \( 10A + B \) must be a multiple of 25. Since \( A \) and \( B \) are digits (0-9), we can analyze possible values for \( C \).

### Step 6: Find possible values for \( C \)
Since \( C \) is a digit, the possible values for \( C \) are 0, 1, 2, or 3 (as \( 25C \) must be a two-digit number).

### Step 7: Test values for \( C \)
1. **If \( C = 0 \)**:
\[ 10A + B = 0 \quad \text{(not valid since A and B must be digits)} \]

2. **If \( C = 1 \)**:
\[ 10A + B = 25 \quad \Rightarrow \quad A = 2, B = 5 \]

3. **If \( C = 2 \)**:
\[ 10A + B = 50 \quad \Rightarrow \quad A = 5, B = 0 \]

4. **If \( C = 3 \)**:
\[ 10A + B = 75 \quad \Rightarrow \quad A = 7, B = 5 \quad \text{(not valid since B cannot be 5)} \]

### Step 8: Conclusion
The valid pairs we found are:
- For \( C = 1 \): \( A = 2, B = 5 \)
- For \( C = 2 \): \( A = 5, B = 0 \)

Since the problem states that \( B \) must be a digit that when multiplied by 5 gives \( B \) itself, the only valid solution is:
\[ A = 5, B = 0 \]

Thus, the final answer is:
\[ A = 5, B = 0 \]