The Georgi-Machacek model predicts the existence of four neutral Higgs bosons, one of which can be identified as the 125-GeV Higgs boson. The latest Higgs data favor the parameter space of small mixing angle alpha between the two custodial singlets of the model. The other two neutral Higgs bosons belong respectively to the custodial triplet and quintet. We study the general decay and production properties of these particles in the small-alpha scenario. Constraints on the SU(2)_L triplet vacuum expectation value are obtained as a function of the exotic Higgs boson masses using latest ATLAS data of various search channels for additional neutral Higgs bosons.