1. The problem is to divide 5 by \frac{1}{3}.\n\n2. The formula for dividing by a fraction is to multiply by its reciprocal. That is, \n$$a \div \frac{b}{c} = a \times \frac{c}{b}$$\n\n3. Applying this to our problem: \n$$5 \div \frac{1}{3} = 5 \times \frac{3}{1}$$\n\n4. Multiply 5 by 3: \n$$5 \times 3 = 15$$\n\n5. Therefore, \n$$5 \div \frac{1}{3} = 15$$\n\nThis means 5 divided by one-third equals 15.