When dividing fractions, you can multiply the first fraction by the reciprocal of the second fraction. In this case, 1/5 ÷ 1/5 can be rewritten as 1/5 * 5/1. Multiplying the numerators (1 * 5) gives us 5, and multiplying the denominators (5 * 1) gives us 5. Therefore, the answer is 5/5, which simplifies to 1.