85971 ÷ 5 = 17194 R1
Alright, let's work through the division of 85971 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 (9) of the dividend behind the 0 and repeat the process: 9 / 5

Step 3:
5 goes into 9 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 171
Subtract 5 from 9 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 5

Step 4:
5 goes into 47 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 1719
Subtract 45 from 47 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 5

Step 5:
5 goes into 21 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 17194
Subtract 20 from 21 to get 1.

The final result is 17194 with a remainder of 1.