The metal-insulator transition driven by electronic correlations is one of the most fundamental concepts in condensed matter. In mixed-valence compounds, this transition is often accompanied by charge ordering (CO), resulting in the emergence of complex phases and unusual behaviors. The famous example is the archetypal mixed-valence mineral magnetite, Fe3O4, exhibiting a complex charge-ordering below the Verwey transition, whose nature has been a subject of long-time debates. In our study, using high-resolution X-ray diffraction supplemented by resistance measurements and DFT+DMFT calculations, the electronic, magnetic, and structural properties of recently synthesized mixed-valence Fe4O5 are investigated under pressure to ∼100 GPa. Our calculations, consistent with experiment, reveal that at ambient conditions Fe4O5 is a narrow-gap insulator characterized by the original Verwey-type CO. Under pressure Fe4O5 undergoes a series of electronic and magnetic-state transitions with an unusual compressional behavior above ∼50 GPa. A site-dependent collapse of local magnetic moments is followed by the site-selective insulator-to-metal transition at ∼84 GPa, occurring at the octahedral Fe sites. This phase transition is accompanied by a 2+ to 3+ valence change of the prismatic Fe ions and collapse of CO. We provide a microscopic explanation of the complex charge ordering in Fe4O5 which "unifies" it with the behavior of two archetypal examples of charge- or bond-ordered materials, magnetite and rare-earth nickelates (RNiO3). We find that at low temperatures the Verwey-type CO competes with the "trimeron"/"dimeron" charge ordered states, allowing for pressure/temperature tuning of charge ordering. Summing up the available data, we present the pressure-temperature phase diagram of Fe4O5.