They are all the exact same shape, colour and size.
Using a round stamp, you need to mark the handkerchiefs so that they can all be told apart.
What is the fewest number of times you need to use the stamp?
Just because there are five hand-kerchiefs, it doesn't mean you have to use the stamp five times.
The shape of the stamp and the location that is stamped would enable you to tell the difference between the handkerchiefs.
The handkerchiefs don't have to be stamped with a circle.
How about lining up several handkerchiefs and stamping them in one go?
The answer is '1'.