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 $$(61-9)+(43-9)=52+34=86$$.