To find the count of numbers not divisible by 5 or 7, we first find the total numbers (1000, from 0 to 999). Then we subtract the numbers divisible by 5 and the numbers divisible by 7. Using the principle of inclusion-exclusion, we add back the numbers divisible by both 5 and 7 (i.e., by 35) to avoid double-counting. The count of numbers divisible by 5 is 200 (999/5). The count of numbers divisible by 7 is 142 (999/7). The count of numbers divisible by 35 is 28 (999/35). So, numbers divisible by 5 or 7 = 200 + 142 - 28 = 314. Therefore, numbers not divisible by 5 or 7 = 1000 - 314 = 686.