1. The problem asks to simplify the expression \( \frac{5:2}{3} \).\n2. First, interpret the colon ":" as division, so \(5:2 = \frac{5}{2}\).\n3. Now the expression becomes \( \frac{\frac{5}{2}}{3} \).\n4. Dividing by 3 is the same as multiplying by its reciprocal, so \( \frac{\frac{5}{2}}{3} = \frac{5}{2} \times \frac{1}{3} \).\n5. Multiply the numerators and denominators: \( \frac{5 \times 1}{2 \times 3} = \frac{5}{6} \).\n6. The fraction \( \frac{5}{6} \) is already in simplest form because 5 and 6 have no common factors other than 1.\n\nFinal answer: \( \frac{5}{6} \)