To solve the equation \( \frac{1}{4}(x + 3) = 5 \), follow these steps:
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Eliminate the fraction by multiplying both sides of the equation by 4:
\[ 4 \cdot \frac{1}{4}(x + 3) = 4 \cdot 5 \]
This simplifies to:
\[ x + 3 = 20 \]
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Isolate \( x \) by subtracting 3 from both sides:
\[ x + 3 - 3 = 20 - 3 \]
This simplifies to:
\[ x = 17 \]
So, the solution is:
\[ \boxed{17} \]