1. The problem is to calculate $5$ divided by $\frac{11}{2}$. 2. The formula for dividing by a fraction is to multiply by its reciprocal: $a \div \frac{b}{c} = a \times \frac{c}{b}$. 3. Applying this rule, we get: $$5 \div \frac{11}{2} = 5 \times \frac{2}{11}$$ 4. Multiply the numerators and denominators: $$= \frac{5 \times 2}{11} = \frac{10}{11}$$ 5. So, $5$ divided by $\frac{11}{2}$ equals $\frac{10}{11}$.