13917 ÷ 5 = 2783 R2
Alright, let's work through the division of 13917 by 5 step by step.

Step 1:
5 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 5

Step 2:
5 goes into 13 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 10 from 13 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 5

Step 3:
5 goes into 39 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 27
Subtract 35 from 39 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 5

Step 4:
5 goes into 41 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 278
Subtract 40 from 41 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 5

Step 5:
5 goes into 17 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 2783
Subtract 15 from 17 to get 2.

The final result is 2783 with a remainder of 2.