Five-Dimensional Systems Theory (5DST) proposes a new worldview of systems: all things are systems characterized by the five-dimensional synergy of Boundary, Structure, Reserve, Direction, and Intensity, and the health of a system depends on its five-dimensional synergy degree. Its deep philosophical foundation is the \textbf{Principle of Relativity}: the essence of game and systemic competition lies not in the absolute strength of the subject, but in the relative proportional relationship among multiple subjects and dimensions. This paper further proposes the \textbf{Principle of Complementary Synergy}: homogeneous systems are difficult to form high-intensity synergistic gains, while heterogeneous complementary systems can give rise to high-order synergistic emergence effects. The article systematically expounds the basic worldview of Five-Dimensional Systems Theory, constructing its ontological, epistemological, and methodological systems within a unified theoretical framework. By introducing synergy coefficients as quantitative measurement tools, it realizes computable, evaluable, and dynamically traceable system synergy states. Cross-scale, multi-domain application analyses show that Five-Dimensional Systems Theory can provide modern systems science with a brand-new research paradigm that combines worldview innovation and quantitative operational tools.