We present the hard-band (2-10 keV) X-ray luminosity function (HXLF) of 0.5-2 keV band selected active galactic nuclei (AGN) at high redshift. We have assembled a sample of 141 AGN at 3 < z ≲ 5 from X-ray surveys of different size and depth, in order to sample different regions in the LX - z plane. The HXLF is fitted in the range log LX ˜ 43-45 with standard analytical evolutionary models through a maximum likelihood procedure. The evolution of the HXLF is well described by a pure density evolution, with the AGN space density declining by a factor of ˜10 from z = 3 to 5. A luminosity-dependent density evolution model, which, normally, best represents the HXLF evolution at lower redshift, is also consistent with the data, but a larger sample of low-luminosity (log LX < 44), high-redshift AGN is necessary to constrain this model. We also estimated the intrinsic fraction of AGN obscured by a column density log NH >= 23 to be 0.54 ± 0.05, with no strong dependence on luminosity. This fraction is higher than the value in the Local Universe, suggesting an evolution of the luminous (LX > 1044 erg s-1) obscured AGN fraction from z = 0 to z > 3.