41689 ÷ 5 = 8337 R4
Alright, let's work through the division of 41689 by 5 step by step.

Step 1:
5 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 5

Step 2:
5 goes into 41 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 40 from 41 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 5

Step 3:
5 goes into 16 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 83
Subtract 15 from 16 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 5

Step 4:
5 goes into 18 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 833
Subtract 15 from 18 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: 8337
Subtract 35 from 39 to get 4.

The final result is 8337 with a remainder of 4.