The new (Zn,Mg,Ni,Fe,Cd)Fe2O4 high entropy ferrite with average crystallite size 11.8 nm was synthesized in two stages by annealing of co-precipitated amorphous precursor. The dielectric spectroscopy confirms, that the electrical conductivity and polarization processes are associated with the mobility of electrons in the structure of ferrite. It was concluded, that the both, high frequency complex dielectric permittivity as well as complex magnetic permeability are strongly temperature and frequency dependent. The AC electrical conductivity is associated with quantum mechanical tunneling of electrons and related to the transfer of charge carriers between Fe2+ and Fe3+ ions. Moreover, the microwave absorption properties were determined. The best microwave absorption properties have been confirmed in the frequency range 1.9 to 2.1 GHz for a layer which is 0.8-1 cm thick. For this range, reflection loss (RL) is lower than -25 dB and shielding effectiveness (SE) lower than -50 dB.