5803 ÷ 7 = 829 R0
Alright, let's work through the division of 5803 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 (8) of the dividend behind the 5 and repeat the process: 58 / 7

Step 2:
7 goes into 58 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 56 from 58 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 7

Step 3:
7 goes into 20 2 times with a remainder of 6.
Write down 2 as next digit of of the result. 
Result so far: 82
Subtract 14 from 20 to get 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 7

Step 4:
7 goes into 63 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 829
Subtract 63 from 63 to get 0.

The final result is 829 with a remainder of 0.