1. **Problem Statement:** Find the sum of the largest and smallest 5-digit numbers formed by the digits 2, 0, 6, 1, 9. 2. **Important Rule:** A 5-digit number cannot start with 0 because then it would be a 4-digit number. 3. **Forming the Largest Number:** Arrange digits in descending order, but the first digit cannot be 0. Digits: 9, 6, 2, 1, 0 Largest number = 96210 4. **Forming the Smallest Number:** Arrange digits in ascending order, but the first digit cannot be 0. Digits: 0, 1, 2, 6, 9 Since 0 cannot be first, the smallest number starts with 1, then 0, 2, 6, 9 Smallest number = 10269 5. **Sum:** $$ 96210 + 10269 = 106479 $$ **Final answer:** The sum of the largest and smallest 5-digit numbers formed is $106479$.