Background: Detailed spectroscopy of neutron-rich odd-A Cu isotopes is of great importance for studying the shell evolution in the region of 78Ni. While there is experimental information on excited states in 69−73,77,79Cu isotopes, the information concerning 75Cu is very limited. Purpose: Experimentally observed single-particle, core-coupling, and proton-hole intruder states in 75Cu, will complete the systematics of these states in the chain of isotopes. Method: Excited states in 75Cu were populated in the β decay of 75Ni isotopes. The Ni nuclei were produced by the in-flight fission of 238U projectiles, and were separated, identified, and implanted in a highly segmented Si detector array for the detection of the β-decay electrons. The β-delayed γ rays were detected in a HPGe cluster array. Monte Carlo shell model calculations were performed using the A3DA interaction built on the pfg9/2d5/2 model space for both neutrons and protons. Results: A level scheme of 75Cu was built up to ≈4 MeV by performing a γ−γ coincidence analysis. The excited states below 2 MeV were interpreted based on the systematics of neutron-rich odd-A Cu isotopes and the results of the shell model calculations. Conclusions: The evolution of the single-particle, core-coupling, and proton-hole intruder states in the chain of neutron-rich odd-A Cu isotopes is discussed in the present work, in connection with the newly observed level structure of 75Cu.