78174 ÷ 5 
We're looking to find how many times 5 goes into 78174.

Step 1:
The number 5 fits into 7 1 times, leaving a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 5 from 7 and we're left with 2.
Append the next digit (8) from the dividend to 2 and continue with: 28 / 5

Advancing to step 2:
5 goes into 28 5 times with a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 15.0
Subtract 25 from 28 to get 3.
Append the next digit (1) from the dividend to 3 and continue with: 31 / 5

Advancing to step 3:
31 divided by 5 is 6 with a remainder of 1.
Record the quotient 6 as the next digit in the result. 
Result so far: 156.0
Subtract 30 from 31 to get 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 5

Let's proceed to step 4:
17 divided by 5 is 3 with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 1563.0
Subtract 15 from 17 to get 2.
Include the next digit (4) from the dividend after 2, then repeat: 24 / 5

Going ahead to step 5:
The number 5 fits into 24 4 times, leaving a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 15634.0
Deduct 20 from 24 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 6:
5 can be fit into 40 8 times, resulting in a remainder of 0.
Put 8 as the next digit of the answer. 
Result so far: 15634.8
Subtracting 40 from 40 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.

Moving on to step 7:
When dividing 0 by 5, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 15634.8
If we subtract 0 from 0, we 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.

Step 8:
5 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 15634.8
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.

The quotient of the division is 15634.8, and the remainder is 0.0.