We report the first evidence for the eta_b(2S) using the h_b(2P)->eta_b(2S)gamma transition and the first observation of the h_b(1P)->eta_b(1S)gamma and h_b(2P)->eta_b(1S)gamma transitions. The mass and width of the eta_b(1S) and eta_b(2S) are measured to be m_etab(1S)=(9402.4+-1.5+-1.8)MeV/c^2, m_etab(2S)=(9999.0+-3.5 +2.8-1.9)MeV/c^2 and Gamma_etab(1S)=(10.8 +4.0-3.7 +4.5-2.0)MeV. We also update the h_b(1P) and h_b(2P) mass measurements. We use a 133.4/fb data sample collected at energies near the Upsilon(5S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.