The cluster-reduction method has been used to solve numerically the differential equations for the s-wave Yakubovsky components in the nppp system. Proton scattering on a ³He nucleus has been considered for energies below the three-body threshold in the singlet and triplet spin states of the system. Nucleon-nucleon interaction has been simulated by the MT I-III potential, and the Coulomb interaction between the protons has been taken into account. Effective equations that describe the relative motion of clusters have been derived. The low-energy behavior of phase shifts has been analyzed. The values of ¹A = 8.2 fm and ³A = 7.7 fm have been obtained for, respectively, the singlet and triplet scattering lengths. The calculated phase shifts agree well with experimental data.