35222 ÷ 7 = 5031 R5
Alright, let's work through the division of 35222 by 7 step by step.

Step 1:
7 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 7

Step 2:
7 goes into 35 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 35 from 35 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 7

Step 3:
7 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 50
Subtract 0 from 2 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 7

Step 4:
7 goes into 22 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 503
Subtract 21 from 22 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 7

Step 5:
7 goes into 12 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 5031
Subtract 7 from 12 to get 5.

The final result is 5031 with a remainder of 5.