High-entropy oxide nanofibers, based on equimolar (Cr,Mn,Fe,Co,Ni), (Cr,Mn,Fe,Co,Zn) and (Cr,Mn,Fe,Ni,Zn) combinations, were prepared by electrospinning followed by calcination. The obtained hollow nanofibers exhibited a porous structure consisting of interconnected nearly strain-free (Cr1/5Mn1/5Fe1/5Co1/5Ni1/5)3O4, (Cr1/5Mn1/5Fe1/5Co1/5Zn1/5)3O4 and (Cr1/5Mn1/5Fe1/5Ni1/5Zn1/5)3O4 single crystals with a pure Fd3̄m spinel structure. Oxidation state of the cations at the nanofiber surface was assessed by X-ray photoelectron spectroscopy and cation distributions were proposed satisfying electroneutrality and optimizing octahedral stabilization. The magnetic data are consistent with a distribution of cations that satisfies the energetic preferences for octahedral vs. tetrahedral sites and is random only within the octahedral and tetrahedral sublattices. The nanofibers are ferrimagnets with relatively low critical temperature more similar to cubic chromites and manganites than to ferrites. Replacing the magnetic cations Co or Ni with non-magnetic Zn lowers the critical temperature from 374 K (Cr,Mn,Fe,Co,Ni) to 233 and 105 K for (Cr,Mn,Fe,Ni,Zn) and (Cr,Mn,Fe,Co,Zn), respectively. The latter nanofibers additionally have a low temperature transition to a reentrant spin-glass-like state.