The 5th dimension is the dimension of spatial size and speed of temporal clocks. 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. ‘A Geometry is the study of the invariant properties of a space(time), under transformations within itself’ (Klein) As such, the geometry of the 5th dimension is defined by a co-invariant equation that relates 2 ‘inverse’ parameters, spatial energy and temporal information: SexTi=K, from where a series of invariant properties followed by all systems of the Universe can be deduced: the invariance of formal motions, of actions, of topological forms, of scales and of time ages. This paper will study them in it first part. The second part will prove that ALL systems of the Universe, in all its scales, from the smallest atom to the biggest galaxy, from the simplest cell to the planetary society follow those invariances. Since the 5th dimension and its formal laws and invariances are the ultimate why that unifies the laws of each science that studies the species, cycles, structures and events of each scale of reality.