86291 ÷ 5 = 17258 R1
Alright, let's work through the division of 86291 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 (6) of the dividend behind the 3 and repeat the process: 36 / 5

Step 2:
5 goes into 36 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 17
Subtract 35 from 36 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 5

Step 3:
5 goes into 12 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 172
Subtract 10 from 12 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 5

Step 4:
5 goes into 29 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 1725
Subtract 25 from 29 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 5

Step 5:
5 goes into 41 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 17258
Subtract 40 from 41 to get 1.

The final result is 17258 with a remainder of 1.