Well, science is based on the rational interpretation of our five senses. Other ways of understanding the world include our five senses but also rely on other phenomena, such as our dreams and emotions, and then are subject to somewhat rational but mostly irrational personal and subjective interpretations. Note that irrational is not the same as incorrect, and I don't consider it a pejorative.

I guess as a primary example, art is non-scientific, but it is an equally valid way of communicating the understanding of our experience to others. We understand beauty. The meaning of symbols in our society seems unlikely to ever come under some scientific theory but forms a very large part of our experience. The search for meaning in life is not a scientific one.

It is probably true that science is the only objective, factually accurate, rational, logical, and methodical approach to understanding the world. This does not invalidate other approaches, since we are more than objective, factually accurate, rational, logical, and methodical beings. Your subjective experience is yours and yours alone and totally resistant to the scientific method.