Neural network: Target vector for 'None of the Above' class?

Say, I have a neural network system trained with 5 classes. When new image is given to the system it will give one class as output depending on the input vector. Now, if I use image of 6th class (system was not trained for 6th class), I have to prepare target vector for that image.

Can I set 0 to all 5 classes in the target vector for the image that belong to the 6th class? I think it will give me error: 'incorrect target vector'.

Do we have something from which we can get an output like: the image belongs to 'None of the above' classes based on input vector? is it mandatory to have output class from the trained classes only?

I mean I think, there has to be something like This image do not belong to any classes that you have trained. How can I prepare target vector for an image with the unknown class. I can't train for unknown class because I don't know the characteristic of the unknown class (say, 6th class).

If this is not possible with simple/shallow neural network, I think someone might suggest me to use Deep Neural Network, I don't want to use it because it requires more data to be accurate and I don't have that.

Thanks