To simplify the expression \( 5(2x - 8) - 3(5x - 8) \), we can start by distributing the constants inside the parentheses.
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Distribute \( 5 \) in the first term: \[ 5(2x - 8) = 10x - 40 \]
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Distribute \( -3 \) in the second term: \[ -3(5x - 8) = -15x + 24 \]
Now we can combine these results: \[ 10x - 40 - 15x + 24 \]
Next, we combine like terms:
- The \( x \) terms: \( 10x - 15x = -5x \)
- The constant terms: \( -40 + 24 = -16 \)
Putting it all together, we have: \[ -5x - 16 \]
Thus, the simplified expression is: \[ \boxed{-5x - 16} \]