We need to find the number of multiples of only one of 5 or 7 between 200 and 500 , inclusive.

The number of multiples of any number say $\(x\)$, from 200 and 500, inclusive can be obtained using formula $\(\frac{\text { Last multiple of } x-\text { First multiple of } x}{x}+1\)$

So, the number of multiples of 5 between 200 and 500 , inclusive is $\(\frac{500-200}{5}+1=61\)$, similarly as the first $\(\&\)$ the last multiples of 7 within the given range are $\(203 \& 497\)$ respectively, the number of multiples of 7 between 200 and 500 , inclusive is

$\(\frac{497-203}{7}+1=43\)$ and the number of multiples of 5 as well as 7 i.e. the number of multiples of 35 within the same range is $\(\frac{490-210}{35}+1=8+1=9\)$

Hence the number of multiples of only one of 5 or 7 between 200 and 500 inclusive is $\((61-9)+(43-9)=52+34=86\)$.