Nonequilibrium processes, including physical aging, belong to the most challenging phenomena of glassy dynamics. One of the fundamental problems that needs clarification is the effect of material polarity on the time scale of the structural recovery of glass. The importance of this issue arises from practical applications and recent findings suggesting a substantial contribution of dipole-dipole interactions to the dielectric permittivity spectra of polar glass-formers. Herein, we use dielectric spectroscopy to investigate structural relaxation and aging dynamics of highly polar glass-former 4-[(4,4,5,5,5-pentafluoropentoxy)methyl]-1,3-dioxolan-2-one (FPC), a derivative of propylene carbonate with εs = 180 and μ = 5.1. We show that ε″(tage) data of FPC at Tage < Tg reveal complex behavior resulting from considerable cross-correlation effects. Namely, two characteristic aging time scales, reflecting the evolution of cross-correlation mode and generic structural relaxation toward equilibrium, are obtained at a given Tage. Furthermore, a single stretched exponential behavior of ε″(tage) has been received for weakly polar carvedilol with negligible dipole-dipole interactions.