We present the renormalized perturbation series for the energy spectra of parabolic quantum dots with two to five electrons, taking into consideration the ground and the lowest excited states. A complete classification of asymptotic energy levels is performed and the behaviour of energy levels from the quantum to the semiclassical regime is traced. Comparison between the present results and those from exact numerical Hamiltonian diagonalization indicates a fair accuracy of the proposed method over the whole range of the electron-electron coupling constant and magnetic field values. The results obtained indicate that increasing the number of electrons in a dot leads to more classical behaviour of the system.