16589 ÷ 5 = 3317 R4
Alright, let's work through the division of 16589 by 5 step by step.

Step 1:
5 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 5

Step 2:
5 goes into 16 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 15 from 16 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 5

Step 3:
5 goes into 15 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 33
Subtract 15 from 15 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 5

Step 4:
5 goes into 8 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 331
Subtract 5 from 8 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 5

Step 5:
5 goes into 39 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 3317
Subtract 35 from 39 to get 4.

The final result is 3317 with a remainder of 4.