5402 ÷ 7 = 771 R5
Alright, let's work through the division of 5402 by 7 step by step.

Step 1:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 7

Step 2:
7 goes into 54 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 49 from 54 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 7

Step 3:
7 goes into 50 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 77
Subtract 49 from 50 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 7

Step 4:
7 goes into 12 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 771
Subtract 7 from 12 to get 5.

The final result is 771 with a remainder of 5.