Animal recognition system

We are working on a project which requires us to recognize specific animals and send a signal if it is convinced about which animal it is. For example: I want to ensure that it is my cat and not the one from the neighbors. We are going to use a live feed for this but can provide videos and pictures. We don't want to train data with like 10.000 pictures of the cat but like 5 as it will be a multi user system. Of course when the system is convinced it is a specific animal it can use it to train later on.

My main question is would this even be possible?