Terahertz vibrational spectroscopy has evolved into a powerful tool for the detection and characterization of transition metal sulfate compounds, specifically for its ability to differentiate between various hydrated forms with high specificity. Copper(II) sulfate is one such system where multiple crystalline hydrates have had their terahertz spectra fully assigned, and the unique spectral fingerprints of the forms allows for characterization of multicomponent systems with relative ease. Yet the most commonly occurring form, copper(II) sulfate pentahydrate (CuSO4⋅5H2O), has proven elusive due to the presence of a broad absorption across much of the terahertz region, making the unambiguous identification of its spectral signature difficult. Here it is shown that the sub-100 cm-1 spectrum of CuSO4⋅5H2O is obscured by absorption from adsorbed water, and that controlled drying reveals sharp underlying features. The crystalline composition of the samples was monitored in parallel by X-ray diffraction as a function of drying time, supporting the spectroscopic results. Finally, the terahertz spectrum of CuSO4⋅5H2O was fully assigned using solid-state density functional theory simulations, helping attribute the additional absorptions that appear after excessive drying to formation of CuSO4⋅3H2O.