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