Yes, the fourth and fifth states of matter do exist. The fourth state is plasma and although not found readily on Earth, it can be created in a lab. It is actually the most common state of matter in the universe. An example of plasma would be lightning or the sun.
The fifth state of matter is called Bose-Einstein condensate or BEC. It occurs when matter is frozen to a temperature at or below absolute zero. When this happens, the particles stop behaving individually and collapse onto each other and can be described as a single wavefunction.
The fourth state of matter is called plasma. Plasma is one of the foundational states of matter. It is the most abundant form of ordinary matter in the universe. It is mostly associated with the stars. It does not exist freely on the earth's surface under normal conditions.
The fifth state of matter is called Bose-Einstein Condensate. BEC is formed by cooling a gas of extremely low density. BEC is a gas of atoms so dense and cold that their matter waves lose their individuality and condense into a microscopic coherent atom wave. It occurs at temperatures near absolute zero.