95969 ÷ 6 = 15994 R5
Alright, let's work through the division of 95969 by 6 step by step.

Step 1:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 9 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 2:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 30 from 35 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 3:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 159
Subtract 54 from 59 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Step 4:
6 goes into 56 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 1599
Subtract 54 from 56 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 6

Step 5:
6 goes into 29 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 15994
Subtract 24 from 29 to get 5.

The final result is 15994 with a remainder of 5.