Using 4.5 fb-1 of e+e- annihilation data samples collected at the center-of-mass energies ranging from 4.600 GeV to 4.699 GeV with the BESIII detector at the BEPCII collider, a first study of the semileptonic decays Λc+→pK-e+νe, Λc+→Λ(1520)e+νe and Λc+→Λ(1405)e+νe is performed. The Λc+→pK-e+νe decay is observed with a significance of 8.2σ and the branching fraction is measured to be B(Λc+→pK-e+νe)=(0.88±0.17stat±0.07syst)×10-3. We also report evidence of Λc+→Λ(1520)e+νe and Λc+→Λ(1405)e+νe with significances of 3.3σ and 3.2σ, respectively, and measure B(Λc+→Λ(1520)e+νe)=(1.02±0.52stat±0.11syst)×10-3 and B(Λc+→Λ(1405)[→pK-]e+νe)=(0.42±0.19stat±0.04syst)×10-3. Combining these with the inclusive semileptonic Λc+ branching fraction measured by BESIII, the relative fraction is determined to be [B(Λc+→pK-e+νe)/B(Λc+→Xe+νe)]=(2.1±0.4stat±0.2syst)%, which provides a clear confirmation that semileptonic Λc+ decays are not saturated by the Λℓ+νℓ final state. © 2022 authors. Published by the American Physical Society.