To simplify the expression \( 7(-8f - 2) + 10(-5f + 7) \), we will first distribute the constants through the parentheses.
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Distribute \( 7 \) in the first part: \[ 7(-8f) + 7(-2) = -56f - 14 \]
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Distribute \( 10 \) in the second part: \[ 10(-5f) + 10(7) = -50f + 70 \]
Now, we combine both parts: \[ -56f - 14 - 50f + 70 \]
Next, combine the like terms. For the \( f \) terms: \[ -56f - 50f = -106f \]
For the constant terms: \[ -14 + 70 = 56 \]
Now putting it all together, we get: \[ -106f + 56 \]
So, the final simplified expression is: \[ \boxed{-106f + 56} \]