65629 ÷ 5 = 13125 R4
Alright, let's work through the division of 65629 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 (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: 13
Subtract 15 from 15 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 5

Step 3:
5 goes into 6 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 131
Subtract 5 from 6 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 5

Step 4:
5 goes into 12 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 1312
Subtract 10 from 12 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 5

Step 5:
5 goes into 29 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 13125
Subtract 25 from 29 to get 4.

The final result is 13125 with a remainder of 4.