95291 ÷ 6 = 15881 R5
Alright, let's work through the division of 95291 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 (2) of the dividend behind the 5 and repeat the process: 52 / 6

Step 3:
6 goes into 52 8 times with a remainder of 4.
Write down 8 as next digit of of the result. 
Result so far: 158
Subtract 48 from 52 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 6

Step 4:
6 goes into 49 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 1588
Subtract 48 from 49 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 6

Step 5:
6 goes into 11 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 15881
Subtract 6 from 11 to get 5.

The final result is 15881 with a remainder of 5.