Subtract:
`a(b - 5)` from `b(5 - a)`

Answer

To solve the problem of subtracting \( a(b - 5) \) from \( b(5 - a) \), we will follow these steps:

### Step 1: Write the Expression
We need to subtract \( a(b - 5) \) from \( b(5 - a) \). This can be expressed mathematically as:
\[ b(5 - a) - a(b - 5) \]

### Step 2: Expand the First Expression
Now, we will expand \( b(5 - a) \):
\[ b(5 - a) = b \cdot 5 - b \cdot a = 5b - ab \]

### Step 3: Expand the Second Expression
Next, we will expand \( a(b - 5) \):
\[ a(b - 5) = a \cdot b - a \cdot 5 = ab - 5a \]

### Step 4: Substitute the Expanded Expressions
Now we substitute the expanded expressions back into the original subtraction:
\[ (5b - ab) - (ab - 5a) \]

### Step 5: Distribute the Negative Sign
Distributing the negative sign across the second expression gives us:
\[ 5b - ab - ab + 5a \]

### Step 6: Combine Like Terms
Now, we will combine like terms:
- The \( ab \) terms: \( -ab - ab = -2ab \)
- The constant terms: \( 5b + 5a \)

Putting it all together, we have:
\[ 5a + 5b - 2ab \]

### Final Answer
Thus, the final result of subtracting \( a(b - 5) \) from \( b(5 - a) \) is:
\[ 5a + 5b - 2ab \]

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