Reality has a 5th dimension of spatial size or 'energy' and speed of temporal clocks that carry the information of the Universe in its frequency and form. Both parameters are inverted: when systems grow in size the speed of its clocks, its ‘time cycles’, diminish proportionally, both in biological and physical systems. And vice versa. Smaller clocks tick faster and information processing carried by the frequency of those cycles accelerates, as it happens in chips, particles or life metabolism. Yet the product of the speed of time of Nature's clocks that process information (Ti) and its spatial-energetic size, Se remains the same across those scales: This fact defines the metrics of the 5th dimension: Se x Ti=K. This paper-book summons up 20 years of research in the formalism and conceptual meaning of the 5th dimension: In the first part, we introduce the Fractal Universe, structured across the 5th dimension and the life-death cycle of all its entities, which exist traveling through 3 scales of the 5th dimension (so for example, we human beings live through 3 scales, the cellular, seminal scale, the organic scale and the social scale, before we return back to the cellular level in the process of death.) In the second part we introduce both, its mathematical formalism, which redefines the 5 postulates of non-euclidean geometry and its logic formalism, which defines 5 arrows of time, one for each Dimension, creating a ternary logic of multiple causality and complex symmetries. Then we use this upgraded mathematical and logic formalism to define the co-invariant laws of motion and form that all systems of the Universe follow, as they exist through those scales. We show this to be the case for the main species of reality, from strings to the Universe as a whole; from the simplest molecule to the more complex society. Finally in the III and IV part we study physical and biological systems under those invariant laws, resolving most of the questions unanswered by previous, simpler 4D formalisms. In other papers, available at viXra we apply those laws also to the study of social and historic cycles, as humans also obey the same co-invariances of all Complementary systems of energy and information, made to the image and likeness of the whole.