62966 ÷ 5 = 12593 R1
Alright, let's work through the division of 62966 by 5 step by step.

Step 1:
5 goes into 6 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 6 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 5

Step 2:
5 goes into 12 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 10 from 12 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 5

Step 3:
5 goes into 29 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 125
Subtract 25 from 29 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: 1259
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: 12593
Subtract 15 from 16 to get 1.

The final result is 12593 with a remainder of 1.