5. Among the positive integers less than 1000, the number of integers that are divisible by 5 or 7, but not by 35, is ( ).
(A) 285
(B) 313
(C) 341
(D) 369
5.A.

If $[x]$ represents the integer part of the positive number $x$, then among the 999 positive integers less than 1000, there are $\left[\frac{999}{5}\right]$ numbers divisible by 5, and $\left[\frac{999}{7}\right]$ numbers divisible by 7. The numbers that are divisible by both 5 and 7 are $\left[\frac{999}{5 \times 7}\right]$. Therefore, the number of numbers that meet the criteria is
$$
\left[\frac{999}{5}\right]+\left[\frac{999}{7}\right]-2 \times\left[\frac{999}{5 \times 7}\right]=285 .
$$