52519 ÷ 4 = 13129 R3
Alright, let's work through the division of 52519 by 4 step by step.

Step 1:
4 goes into 5 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 5 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 4

Step 2:
4 goes into 12 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 12 from 12 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 4

Step 3:
4 goes into 5 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 131
Subtract 4 from 5 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 4

Step 4:
4 goes into 11 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 1312
Subtract 8 from 11 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 4

Step 5:
4 goes into 39 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 13129
Subtract 36 from 39 to get 3.

The final result is 13129 with a remainder of 3.