5365 ÷ 3 = 1788 R1
Alright, let's work through the division of 5365 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 (3) of the dividend behind the 2 and repeat the process: 23 / 3

Step 2:
3 goes into 23 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 17
Subtract 21 from 23 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 3

Step 3:
3 goes into 26 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 178
Subtract 24 from 26 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 3

Step 4:
3 goes into 25 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 1788
Subtract 24 from 25 to get 1.

The final result is 1788 with a remainder of 1.