61677 ÷ 5 
The aim is to understand the frequency of 5 in 61677.

Step 1:
If we divide 6 by 5, we get 1 and a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 5 away from 6, we end up with 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 5

Moving on to step 2:
5 can be fit into 11 2 times, resulting in a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 12.0
If we subtract 10 from 11, we get 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 5

Moving on to step 3:
If we divide 16 by 5, we get 3 and a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 123.0
Subtract 15 from 16 to get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 5

Moving on to step 4:
5 goes into 17 3 times with a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 1233.0
If we subtract 15 from 17, we get 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 5

Let's proceed to step 5:
The number 5 fits into 27 5 times, leaving a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 12335.0
If we take 25 away from 27, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 6:
The number 5 fits into 20 4 times, leaving a remainder of 0.
The number 4 becomes the next digit in our result. 
Result so far: 12335.4
The remainder is 0 after subtracting 20 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 7:
The number 5 fits into 0 0 times, leaving a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 12335.4
Deduct 0 from 0 and we're left 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 8:
The number 5 fits into 0 0 times, leaving a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 12335.4
The remainder is 0 after subtracting 0 from 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 final result is 12335.4 with a remainder of 0.0.