5789 ÷ 9 = 643 R2
Alright, let's work through the division of 5789 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 (7) of the dividend behind the 5 and repeat the process: 57 / 9

Step 2:
9 goes into 57 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 54 from 57 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 9

Step 3:
9 goes into 38 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 64
Subtract 36 from 38 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 9

Step 4:
9 goes into 29 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 643
Subtract 27 from 29 to get 2.

The final result is 643 with a remainder of 2.