5034 ÷ 9 = 559 R3
Alright, let's work through the division of 5034 by 9 step by step.

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 (0) of the dividend behind the 5 and repeat the process: 50 / 9

Step 2:
9 goes into 50 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 45 from 50 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 9

Step 3:
9 goes into 53 5 times with a remainder of 8.
Write down 5 as next digit of of the result. 
Result so far: 55
Subtract 45 from 53 to get 8.
Bring next digit (4) of the dividend behind the 8 and repeat the process: 84 / 9

Step 4:
9 goes into 84 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 559
Subtract 81 from 84 to get 3.

The final result is 559 with a remainder of 3.