5013 ÷ 3 = 1671 R0
Alright, let's work through the division of 5013 by 3 step by step.

Step 1:
3 goes into 5 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 3 from 5 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 3

Step 2:
3 goes into 20 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 18 from 20 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 3

Step 3:
3 goes into 21 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 167
Subtract 21 from 21 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 3

Step 4:
3 goes into 3 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1671
Subtract 3 from 3 to get 0.

The final result is 1671 with a remainder of 0.