imc

Multiples of $5$ will always end in $0$ or $5$, and since the numbers have to be a three-digit numbers (otherwise it would be a two-digit number), it cannot start with 0, narrowing our choices to 3-digit numbers starting with $5$. Since the numbers must be divisible by 7, all possibilities have to be in the range from $7\cdot 72$ to $7\cdot 85$ inclusive. $85-72+1=14$. $\boxed{14}$. (Add 1 to include 72)