75003 ÷ 7 = 10714 R5
No problem, we've got 75003 and 7 for the division.

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

Step 2:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 5 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: 107
Subtract 49 from 50 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 7

Step 4:
7 goes into 10 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1071
Subtract 7 from 10 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 7

Step 5:
7 goes into 33 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 10714
Subtract 28 from 33 to get 5.

The final result is 10714 with a remainder of 5.