6309 ÷ 5 = 1261 R4
Let's divide 6309 by 5.

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 (3) of the dividend behind the 1 and repeat the process: 13 / 5

Step 2:
5 goes into 13 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 10 from 13 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 5

Step 3:
5 goes into 30 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 126
Subtract 30 from 30 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 5

Step 4:
5 goes into 9 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1261
Subtract 5 from 9 to get 4.

The final result is 1261 with a remainder of 4.