1. **State the problem:** Add the numbers 7192 and 5519. 2. **Add the units place:** $2 + 9 = 11$. Write 1 and carry over 1. 3. **Add the tens place:** $9 + 1 = 10$, plus the carried over 1 equals $11$. Write 1 and carry over 1. 4. **Add the hundreds place:** $1 + 5 = 6$, plus the carried over 1 equals $7$. Write 7. 5. **Add the thousands place:** $7 + 5 = 12$. Write 12. 6. **Combine all digits:** The sum is $12711$. **Final answer:** $12711$