Yes, let me break it down for you. 11 is a multiple of 11, and 1111, or 11 100+11 is also a multiple of 11. You can keep going and conclude that every even number of ones can be a multiple of 11 (e.g. 11,1111,111111,...). If every even number of ones is a multiple of 11, an odd number of ones is 10 an even number of ones+1, which is 1 mod 11 and not divisible by 11. Therefore, our number must have an even number of 5's which is also divisible by 9. The smallest number of 5's which satisfies this is 18, so the answer is
555555555555555555!