To solve the expression \( 67 - 5 \times (8 - 5)^2 \), we follow the order of operations (PEMDAS/BODMAS):
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Parentheses: Calculate \( (8 - 5) \): \[ 8 - 5 = 3 \]
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Exponentiation: Now calculate \( (3)^2 \): \[ 3^2 = 9 \]
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Multiplication: Next, multiply by 5: \[ 5 \times 9 = 45 \]
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Subtraction: Finally, subtract from 67: \[ 67 - 45 = 22 \]
So, the final result is: \[ \boxed{22} \]