1. The problem is to divide 5 by $\frac{1}{2}$, i.e., calculate $5 \div \frac{1}{2}$. 2. The rule for division by a fraction is to multiply by its reciprocal. That means: $$a \div \frac{b}{c} = a \times \frac{c}{b}$$ 3. Here, the divisor is $\frac{1}{2}$. Its reciprocal is $2$ because: $$\frac{1}{\frac{1}{2}} = 2$$ 4. Rescale the divisor to 1 by multiplying both dividend and divisor by 2: $$5 \div \frac{1}{2} = (5 \times 2) \div \left(\frac{1}{2} \times 2\right)$$ 5. Simplify the divisor: $$\frac{1}{2} \times 2 = \cancel{\frac{1}{2}} \times \cancel{2} = 1$$ 6. So the problem becomes: $$10 \div 1 = 10$$ 7. Therefore, the answer is: $$\boxed{10}$$ This means dividing 5 by $\frac{1}{2}$ is the same as multiplying 5 by 2, which equals 10.