15966 ÷ 5 = 3193 R1
Alright, let's work through the division of 15966 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 (5) of the dividend behind the 1 and repeat the process: 15 / 5

Step 2:
5 goes into 15 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 15 from 15 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 5

Step 3:
5 goes into 9 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 31
Subtract 5 from 9 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 5

Step 4:
5 goes into 46 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 319
Subtract 45 from 46 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 5

Step 5:
5 goes into 16 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 3193
Subtract 15 from 16 to get 1.

The final result is 3193 with a remainder of 1.