Explore the fifth lecture in a series on methods for studying abelian actions and centralizers in dynamical systems. Delve into the concepts of transitive centralizers and fibered partially hyperbolic systems. Examine how these topics relate to the broader study of smooth centralizers and their connection to algebraic dynamical systems. Gain insights into the ongoing research aimed at understanding when dynamical systems with large centralizers are essentially algebraic in nature. Build upon the knowledge from previous lectures to further investigate the rigidity properties of abelian actions and centralizers in various mathematical contexts.