559 ÷ 5 = 111 R4
Alright, let's work through the division of 559 by 5 step by step.

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

Step 2:
5 goes into 5 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 5 from 5 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 5

Step 3:
5 goes into 9 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 111
Subtract 5 from 9 to get 4.

The final result is 111 with a remainder of 4.