First consider an easier expression such as 10⁵ – 560. Doing the computation yields 99,440, which has 2 9's followed by 440. 
From this, we can extrapolate that 10²⁵ – 560 will have a string of 22 9's followed by 440. 
Now simply apply your divisibility rules:
You might want to skip 11 first  because there is no straight forward rule for divisibility by 11. You can always return to this if necessary. [One complex way to test divisibility by 11 is to assign opposite signs to adjacent digits and then to add them to see if they add up to 0. For example, we know that 121 is divisible by 11 because -1 +2 -1 equals zero. In our case, the twenty-two 9s, when assigned opposite signs, will add up to zero, and so will the digits of 440, since +4 -4 +0 equals zero.]
 
If the last three digits of the number are divisible by 8, the number is divisible by 8. Since 440 is divisible by 8, the entire expression is divisible by 8.
If the last two digits of the number are divisible by 4, the number is divisible by 4. Since 40 is divisible by 4, the enter expression is divisible by 4.
If a number ends in 0 or 5, it is divisible by 5. Since the expression ends in 0, it is divisible by 5.
For a number to be divisible by three, the sum of the digits must be divisible by three. The sum of the 22 9's will be divisible by three but when you add the sum of the last three digits, 8 (4 + 4 + 0), the result will not be divisible by 3. Thus, the expression will NOT be divisible by 3.
 
The correct answer is E.