High entropy oxide (HEO) is a new class of lithium-ion battery anode with high specific capacity and excellent cyclability. The beauty of HEO lies in the unique tailorable properties with respect to tunable chemical composition, which enables the use of infinite element combinations to develop new electrode materials. This study synthesizes a series of Co-free spinel-type HEOs via a facile hydrothermal method. Based on quaternary medium-entropy (CrNiMnFe)3O4, the fifth elements of V, Mg, and Cu are added, and their ability to form single-phase HEOs is investigated. It is demonstrated that the chemical composition of HEOs is critical to the phase purity and corresponding charge–discharge performance. The oxygen vacancy concentration seems to be decisive for the rate capability and reversibility of the HEO electrodes. An inactive spectator element is not necessary for achieving high cyclability, given that the phase purity of the HEO is wisely controlled. The single-phase (CrNiMnFeCu)3O4 shows a great high-rate capacity of 480 mAh g−1 at 2000 mA g−1 and almost no capacity decay after 400 cycles. Its phase transition behavior during the lithiation/delithiation process is characterized with operando X-ray diffraction. A (CrNiMnFeCu)3O4||LiNi0.8Co0.1Mn0.1O2 cell is constructed with 590 Wh kg−1 (based on electrode materials) gravimetric energy density.