7642 ÷ 5 = 1528 R2
Alright, let's work through the division of 7642 by 5 step by step.

Step 1:
5 goes into 7 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 5 from 7 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 5

Step 2:
5 goes into 26 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 25 from 26 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 5

Step 3:
5 goes into 14 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 152
Subtract 10 from 14 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 5

Step 4:
5 goes into 42 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 1528
Subtract 40 from 42 to get 2.

The final result is 1528 with a remainder of 2.