The cluster-reduction method is used to solve numerically the differential equations for the s-wave Yakubovsky components characterizing the nnpp system in the 5 = 2 spin state. Elastic deuteron-deuteron scattering is analyzed for the case where nucleon-nucleon interaction is simulated by the MTI-III potentials. Effective equations describing the relative motion of clusters is derived. The scattering length and phase shifts for low-energy deuteron-deuteron scattering are calculated.