  Assuming that the time-evolution of the self-consistent mean field is
determined by five pairs of collective coordinate and collective momentum, we
microscopically derive the collective Hamiltonian for low-frequency quadrupole
modes of excitation. We show that the five-dimensional collective Schr\"odinger
equation is capable of describing large-amplitude quadrupole shape dynamics
seen as shape coexistence/mixing phenomena. We focus on basic ideas and recent
advances of the approaches based on the time-dependent mean-field theory, but
relations to other time-independent approaches are also briefly discussed.
