To simplify the equation \( 12 - 2(x + 1) = 5 \), we can follow these steps:
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Distribute the \(-2\) into \( (x + 1) \): \[ 12 - 2x - 2 = 5 \]
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Combine the constant terms on the left side: \[ 10 - 2x = 5 \]
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Rearranging gives us: \[ -2x + 10 = 5 \]
So the simplified version is: \[ -2x + 10 = 5 \]
Therefore, the correct answer is \( \text{A. } -2x + 10 = 5 \).