To instantly find the remainder of any massive integer divided by 5, look exclusively at the final digit:
- If the last digit is $\lt 5$, the remainder is the last digit itself.
- If the last digit is $\ge 5$, the remainder is $(\text{last digit} - 5)$.
For 1003, the last digit is 3, which is less than 5. Hence, the remainder is immediately 3.