5. (10 points) The sum of all natural numbers less than 200 and coprime with 200 is $\qquad$
【Solution】Solution: $200=5^{2} \times 2^{3}$,
To be coprime with 200, it must be: neither a multiple of 2 nor a multiple of 5. The sum of odd numbers from 1 to 199 is: $\frac{(1+199) \times 100}{2}$
$$
\begin{array}{l}
=100 \times 100 \\
=10000,
\end{array}
$$

Among them, the sum of multiples of 5 (odd multiples) is:
The largest multiple of 5 is $5 \times 39$,
$$
\begin{array}{l}
5 \times \frac{(1+39) \times 20}{2} \\
=5 \times 400 \\
=2000, \\
10000-2000=8000 ;
\end{array}
$$

Answer: The sum of all natural numbers less than 200 and coprime with 200 is 8000. Therefore, the answer is: 8000.