- We need to find the smallest natural number 'x' such that \( (1800 - x) \equiv 5 \mod (7, 11, 23) \).
- This means \( (1800 - x) - 5 \) should be divisible by 7, 11, and 23.
- First, calculate \( 1800 - 5 = 1795 \).
- We need \( 1795 - x \) divisible by the least common multiple (LCM) of 7, 11, and 23.
- Calculate the LCM: LCM(7, 11, 23) = 1771.
- Find x such that 1795 - x = 1771k for some integer k.
- The smallest positive \( x = 1795 - 1771 \).
- Therefore, \( x = 24 \).

**The correct option is: Option 4 - 24. ✅**

**YOUR ANSWER IS RIGHT**