To determine how many whole birthday cards Noel made, we can start by finding out how many cards he can make in the time he worked.
Noel worked for \( \frac{11}{12} \) hours, and each card takes \( \frac{1}{6} \) hours to make.
We can calculate the number of cards he made by dividing the total time worked by the time it takes to make one card:
\[ \text{Number of cards} = \frac{\frac{11}{12}}{\frac{1}{6}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Number of cards} = \frac{11}{12} \times \frac{6}{1} = \frac{11 \times 6}{12} = \frac{66}{12} = \frac{11}{2} = 5.5 \]
Since he made \( 5.5 \) cards, the number of whole cards he made is \( 5 \).
Thus, the answer is C) 5 cards.