5. \( 5 \frac{2}{6}-2 \frac{5}{6}= \)

First, let’s convert the mixed numbers into improper fractions. For \( 5 \frac{2}{6} \), we multiply \(5\) by \(6\) (which gives \(30\)) and then add \(2\) to get \(32\), resulting in \( \frac{32}{6} \). For \( 2 \frac{5}{6} \), we do the same: \(2 \times 6\) gives \(12\), plus \(5\) results in \( \frac{17}{6} \). Next, we subtract the second fraction from the first: \[ \frac{32}{6} - \frac{17}{6} = \frac{32 - 17}{6} = \frac{15}{6} \] Now, simplify \( \frac{15}{6} \) to \( \frac{5}{2} \) or \( 2 \frac{1}{2} \). So the final answer is \( 2 \frac{1}{2} \).