jmc

To be divisible by both 5 and 11, an integer must be a multiple of 55. The smallest three-digit multiple of 55 is $2\cdot 55=110,$ and the largest three-digit multiple of 55 is $18\cdot 55=990$. So we can count the number of integers by the number of multiples, $2,3,\dots ,17,18$, of which there are $\boxed{17}$.