13001 ÷ 5 = 2600 R1
Alright, let's work through the division of 13001 by 5 step by step.

Step 1:
5 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 5

Step 2:
5 goes into 13 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 10 from 13 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 5

Step 3:
5 goes into 30 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 26
Subtract 30 from 30 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 5

Step 4:
5 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 260
Subtract 0 from 0 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 5

Step 5:
5 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 2600
Subtract 0 from 1 to get 1.

The final result is 2600 with a remainder of 1.