85679 ÷ 5 = 17135 R4
Alright, let's work through the division of 85679 by 5 step by step.

Step 1:
5 goes into 8 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 8 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 5

Step 2:
5 goes into 35 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 17
Subtract 35 from 35 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 5

Step 3:
5 goes into 6 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 171
Subtract 5 from 6 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 5

Step 4:
5 goes into 17 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 1713
Subtract 15 from 17 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 5

Step 5:
5 goes into 29 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 17135
Subtract 25 from 29 to get 4.

The final result is 17135 with a remainder of 4.