The given expression is:
\[ (-5x + 8) - (2 + x) \]
First, distribute the negative sign across the second set of parentheses:
\[ = -5x + 8 - 2 - x \]
Combine the like terms in the expression:
This gives us:
\[ = -6x + 6 \]
The simplified expression is:
\[ \boxed{-6x + 6} \]
Thus, the correct answer is A.
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