6871 ÷ 5 = 1374 R1
Alright, let's work through the division of 6871 by 5 step by step.

Step 1:
5 goes into 6 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 6 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 5

Step 2:
5 goes into 18 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 15 from 18 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 5

Step 3:
5 goes into 37 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 137
Subtract 35 from 37 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 5

Step 4:
5 goes into 21 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 1374
Subtract 20 from 21 to get 1.

The final result is 1374 with a remainder of 1.