Compositionally complex doping of spinel oxides toward high-entropy oxides is expected to enhance their electrochemical performance substantially. We successfully prepared high-entropy compounds, i.e. the oxide (Zn0.25Mg0.25Co0.25Cu0.25)Fe2O4 (HEOFe), lithiated oxyfluoride Li0.5(Zn0.25Mg0.25Co0.25Cu0.25)0.5Fe2O3.5F0.5 (LiHEOFeF), and lithiated oxychloride Li0.5(Zn0.25Mg0.25Co0.25Cu0.25)0.5Fe2O3.5Cl0.5 (LiHEOFeCl) with a spinel-based cubic structure by ball milling and subsequent heat treatment. The products exhibit particles with sizes from 50 to 200 nm with a homogeneous atomic distribution. The average elemental composition of the samples is close to the nominal value. 57Fe Mössbauer spectroscopy revealed that incorporating Li and F or Cl and forming oxygen defects do not influence the redistribution of Fe3+ cations over the spinel lattice sites and result in their preferred octahedral coordination. Electrochemical measurements carried out using 2032-coin cells with a Li-metal anode have shown voltammetric charge capacities of 450, 694, and 593 mA h g-1 for HEOFe, LiHEOFeCl, and LiHEOFeF, respectively. The best electrochemical performance of LiHEOFeCl was ascribed to its smallest particle size. Galvanostatic chronopotentiometry at 1C rate confirmed high initial charge capacities for all the samples but galvanostatic curves exhibited capacity decay over 100 charging/discharging cycles. Raman spectroelectrochemical analysis conducted on the LiHEOFeF sample proved the reversibility of the electrochemical process for initial charging/discharging cycles. Electrochemical impedance spectroscopy revealed the lowest initial charge transfer resistance for LiHEOFeCl and its gradual decrease both for LiHEOFeCl and LiHEOFeF during galvanostatic cycling, whereas the charge transfer resistance of HEOFe slightly increases over 100 galvanostatic cycles due to the different mechanism of the electrochemical reduction.