5566 ÷ 8 = 695 R6
No problem, we've got 5566 and 8 for the division.

Step 1:
8 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 8

Step 2:
8 goes into 55 6 times with a remainder of 7.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 48 from 55 to get 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 8

Step 3:
8 goes into 76 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 69
Subtract 72 from 76 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 8

Step 4:
8 goes into 46 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 695
Subtract 40 from 46 to get 6.

The final result is 695 with a remainder of 6.