5503 ÷ 9 = 611 R4
No problem, we've got 5503 and 9 for the division.

Step 1:
9 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 / 9

Step 2:
9 goes into 55 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 54 from 55 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 9

Step 3:
9 goes into 10 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 61
Subtract 9 from 10 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 9

Step 4:
9 goes into 13 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 611
Subtract 9 from 13 to get 4.

The final result is 611 with a remainder of 4.