66665 ÷ 7 = 9523 R4
Alright, let's work through the division of 66665 by 7 step by step.

Step 1:
7 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 7

Step 2:
7 goes into 66 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 63 from 66 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 7

Step 3:
7 goes into 36 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 95
Subtract 35 from 36 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 7

Step 4:
7 goes into 16 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 952
Subtract 14 from 16 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 7

Step 5:
7 goes into 25 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 9523
Subtract 21 from 25 to get 4.

The final result is 9523 with a remainder of 4.