From December 2019 to June 2021, the BESIII experiment collected approximately 5.85 fb−1 of data at center-of-mass energies between 4.61 and 4.95 GeV. This is the highest collision energy BEPCII has reached to date. The accumulated annihilation data samples are useful for studying charmonium(-like) states and charmed-hadron decays. By adopting a novel method of analyzing the production of pairs in annihilation, the center-of-mass energies are measured with a precision of 0.6 MeV. Integrated luminosities are measured with a precision of better than 1% by analyzing the events of large-angle Bhabha scattering. These measurements provide important inputs to analyses based on these data samples. © 2022 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.