Pressure-induced dehydration transitions of CoSO4 center dot 6H(2)O and CoSO4 center dot 7H(2)O were observed by in-situ powder X-ray diffraction at high pressure. Both transformed to an unreported high-pressure phase, CoSO4 center dot 5H(2)O at 1-2 GPa, whose crystal structure was determined by single crystal X-ray diffraction. The results show that CoSO4 center dot 5H(2)O has a triclinic structure with cell parameters of a = 6.4436 (6) angstrom, b = 10.2300 (12) angstrom, c = 5.1914 (6) angstrom, alpha = 91.953 (10)degrees, beta = 87.084 (10)degrees, gamma = 101.085 (10)degrees, V = 335.28 (6) angstrom(3), at 1.3 GPa, and it has a layered crystal structure consisting of [Co(H2O)(6)] and [Co(H2O)(4)(SO4)(2)]. This structure is distinct from previously reported crystal structures of MSO4 center dot 5H(2)O (M = Mg, Mn, Fe, Cu) in a metal coordination environment. The compressibility of CoSO4 center dot 5H(2)O was fitted by the 3rd-order Birch-Murnaghan equation of state, yielding K-0 = 25 (+/- 2) GPa, K-0' = 7.4 (+/- 0.5), V-0 = 352 (+/- 2) angstrom(3).