To solve for \( y \) in the equation \( 5 = 3(y - 4) - 4 \), we can follow these steps:
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Start with the original equation:
\[ 5 = 3(y - 4) - 4 \]
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Distribute the \( 3 \) on the right side:
\[ 5 = 3y - 12 - 4 \]
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Combine the constant terms on the right side:
\[ 5 = 3y - 16 \]
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Add \( 16 \) to both sides to isolate the term with \( y \):
\[ 5 + 16 = 3y \]
\[ 21 = 3y \]
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Divide both sides by \( 3 \) to solve for \( y \):
\[ y = \frac{21}{3} = 7 \]
Thus, the solution is:
\[ \boxed{7} \]