Let's divide 105588 by 5
We want to divide 105588 by 5.

Advancing to step 1:
When dividing 1 by 5, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 5

Let's proceed to step 2:
If we divide 10 by 5, we get 2 and a remainder of 0.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we take 10 away from 10, we end up with 0.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 5

On to step 3:
5 divided by 5 is 1 with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 21.0
Deduct 5 from 5 and we're left with 0.
Append the next digit (5) from the dividend to 0 and continue with: 5 / 5

Let's proceed to step 4:
If we divide 5 by 5, we get 1 and a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 211.0
Deduct 5 from 5 and we're left with 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 5

Going ahead to step 5:
The number 5 fits into 8 1 times, leaving a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 2111.0
The remainder is 3 after subtracting 5 from 8.
Append the next digit (8) from the dividend to 3 and continue with: 38 / 5

Moving on to step 6:
5 goes into 38 7 times with a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 21117.0
Subtract 35 from 38 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 7:
If we divide 30 by 5, we get 6 and a remainder of 0.
Record the quotient 6 as the next digit in the result. 
Result so far: 21117.6
Subtract 30 from 30 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
0 divided by 5 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 21117.6
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 9:
If we divide 0 by 5, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 21117.6
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 21117.6, and the remainder is 0.0.