5813 ÷ 6 = 968 R5
Let's divide 5813 by 6.

Step 1:
6 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 6

Step 2:
6 goes into 58 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 54 from 58 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 6

Step 3:
6 goes into 41 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 96
Subtract 36 from 41 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Step 4:
6 goes into 53 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 968
Subtract 48 from 53 to get 5.

The final result is 968 with a remainder of 5.