Data Sufficiency

If you want a number's remainder when you divide it by 3, you can sum the digits of the number and take the remainder by 3 of that sum. The sum of the digits of (5)(10^n) is always going to be 5 no matter what n equals, so we only need the value of m. If m = 1, then the digits of (5)(10^n) + m will sum to 6, so the number will be a multiple of 3 and the remainder will be zero. So the answer is B.