89321 ÷ 6 = 14886 R5
Alright, let's work through the division of 89321 by 6 step by step.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 6

Step 2:
6 goes into 29 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 24 from 29 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Step 3:
6 goes into 53 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 148
Subtract 48 from 53 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 6

Step 4:
6 goes into 52 8 times with a remainder of 4.
Write down 8 as next digit of of the result. 
Result so far: 1488
Subtract 48 from 52 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 6

Step 5:
6 goes into 41 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 14886
Subtract 36 from 41 to get 5.

The final result is 14886 with a remainder of 5.