If you count all the things that can happen at extreme conditions (including things that theoretically might happen but have not yet been observed) there are a lot more than five.
I guess you teacher's three were solid, liquid, and gas. You could add plasma as a fourth "classical" state. You can think of a plasma as being a like gas, but where all the electrons have been separated from the nuclei of the atoms, so every particle has its own electric charge. It occurs naturally in lightning strikes, electric sparks, and sometimes in flames.
Unless you just want a list of names, you can't really understand any of the other states of matter without first learning about quantum mechanics.