8261 ÷ 5 = 1652 R1
Alright, let's work through the division of 8261 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 (2) of the dividend behind the 3 and repeat the process: 32 / 5

Step 2:
5 goes into 32 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 30 from 32 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 5

Step 3:
5 goes into 26 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 165
Subtract 25 from 26 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 5

Step 4:
5 goes into 11 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 1652
Subtract 10 from 11 to get 1.

The final result is 1652 with a remainder of 1.