To determine which of the equations has a solution of \( x = -7 \), we'll substitute \( -7 \) into each equation and check if the equation holds true.
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For \( 4x - 23 = 5 \): \[ 4(-7) - 23 = -28 - 23 = -51 \quad (\text{not } 5) \]
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For \( -x + 3 = -4 \): \[ -(-7) + 3 = 7 + 3 = 10 \quad (\text{not } -4) \]
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For \( 5x + 11 = -24 \): \[ 5(-7) + 11 = -35 + 11 = -24 \quad (\text{true}) \]
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For \( -3x - 8 = -29 \): \[ -3(-7) - 8 = 21 - 8 = 13 \quad (\text{not } -29) \]
The equation that has a solution of \( x = -7 \) is: \( 5x + 11 = -24 \).