The classical laws of thermodynamics describe the evolution of energy, entropy, and equilibrium in physical systems, yet they do not explicitly treat information as a physical quantity with thermodynamic status. In this work, I propose the Extended Fifth Law of Thermodynamics, asserting that information acts as a fundamental physical variable governing organization, stability, and the direction of evolution in complex systems. I formalize this principle and introduce a quantity—organizational efficiency, denoted R—defined by the balance between information and entropy. I demonstrate how thisframework unifies phenomena across physics, biology, computation, and artificial intelligence. I develop the mathematical formulation of the law, analyze its implications for non-equilibrium systems, and show how it directly enables the construction of new computational models, including the R-Law AI framework. Examples from machine learning illustrate how information-entropy dynamics shape learning trajectories and structural coherence. I conclude by discussing the broader relevance of the Extended Fifth Law for understanding order formation, self-organization, and intelligence in natural and artificial systems.