95638 ÷ 5 = 19127 R3
Alright, let's work through the division of 95638 by 5 step by step.

Step 1:
5 goes into 9 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 9 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 5

Step 2:
5 goes into 45 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 45 from 45 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 5

Step 3:
5 goes into 6 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 191
Subtract 5 from 6 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 5

Step 4:
5 goes into 13 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 1912
Subtract 10 from 13 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 5

Step 5:
5 goes into 38 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 19127
Subtract 35 from 38 to get 3.

The final result is 19127 with a remainder of 3.