Answer
$400$ numbers.
Work Step by Step
For any number from 1 to 1000, there is a $1/2$ chance of it being divisible by 2 and a $1/5$ chance of it being divisible by 5. As al residues are evenly distributed from 1 to 1000, we can find the proportion of relatively prime numbers by doing $(1-1/2)(1-1/5) =2/5$, so the answer is $1000 * 2/5 = 400$
