To simplify the expression \(\frac{8a + 8}{a - 3} - 5\), we will first rewrite \( -5 \) as a fraction with a common denominator.
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Rewrite \(-5\) with a denominator of \(a - 3\): \[ -5 = -\frac{5(a - 3)}{a - 3} = -\frac{5a - 15}{a - 3} \]
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Now, we can rewrite the original expression: \[ \frac{8a + 8}{a - 3} - \frac{5a - 15}{a - 3} \]
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With a common denominator, we can combine the fractions: \[ \frac{(8a + 8) - (5a - 15)}{a - 3} \]
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Distributing the negative sign in the numerator: \[ = \frac{8a + 8 - 5a + 15}{a - 3} \] \[ = \frac{(8a - 5a) + (8 + 15)}{a - 3} \] \[ = \frac{3a + 23}{a - 3} \]
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The expression \(\frac{3a + 23}{a - 3}\) is the simplified form, and there are no common factors to reduce further.
Thus, the simplified expression is: \[ \frac{3a + 23}{a - 3} \]