We look at the division of 5319 by 42 
We're looking to find how many times 42 goes into 5319.

Going ahead to step 1:
The number 42 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (3) from the dividend after 5, then repeat: 53 / 42

Going ahead to step 2:
42 can be fit into 53 1 times, resulting in a remainder of 11.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 42 from 53 leaves us with 11.
Take the next digit (1) from the dividend and append it to 11, then repeat: 111 / 42

Let's proceed to step 3:
If we divide 111 by 42, we get 2 and a remainder of 27.
Put 2 as the next digit of the answer. 
Result so far: 12.0
If we take 84 away from 111, we end up with 27.
Grab the next digit (9) from the dividend, add it to 27, then carry on: 279 / 42

Moving on to step 4:
42 goes into 279 6 times with a remainder of 27.
Put 6 as the next digit of the answer. 
Result so far: 126.0
Deduct 252 from 279 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 5:
The number 42 fits into 270 6 times, leaving a remainder of 18.
Use 6 as the next digit of our solution. 
Result so far: 126.6
Deduct 252 from 270 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 6:
42 can be fit into 180 4 times, resulting in a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 126.64
If we take 168 away from 180, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 7:
When dividing 120 by 42, we get 2 with a remainder of 36.
Put 2 as the next digit of the answer. 
Result so far: 126.642
Deduct 84 from 120 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Let's proceed to step 8:
42 goes into 360 8 times with a remainder of 24.
The number 8 becomes the next digit in our result. 
Result so far: 126.6428
The remainder is 24 after subtracting 336 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 9:
When dividing 240 by 42, we get 5 with a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 126.64285
The remainder is 30 after subtracting 210 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 10:
The number 42 fits into 300 7 times, leaving a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 126.642857
Subtract 294 from 300 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 11:
42 goes into 60 1 times with a remainder of 18.
Put 1 as the next digit of the answer. 
Result so far: 126.6428571
If we take 42 away from 60, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 12:
42 goes into 180 4 times with a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 126.64285714
Deduct 168 from 180 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 126.64285714 with a balance of 1.2e-08.