We present the hard-band ($2-10,mathrm{keV}$) X-ray luminosity function (HXLF) of $0.5-2,mathrm{keV}$ band selected AGN at high redshift. We have assembled a sample of 141 AGN at $3<zlesssim5$ from X-ray surveys of different size and depth, in order to sample different regions in the $ L_X - z$ plane. The HXLF is fitted in the range $mathrm{logL_Xsim43-45}$ 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 $sim10$ 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 ($mathrm{logL_X}<44$), high-redshift AGN is necessary to constrain this model. We also estimated the intrinsic fraction of AGN obscured by a column density $mathrm{logN_H}geq23$ to be $0.54pm0.05$, with no strong dependence on luminosity. This fraction is higher than the value in the Local Universe, suggesting an evolution of the luminous ($mathrm{L_X>10^{44}mathrm{erg,s^{-1}}}$) obscured AGN fraction from $z=0$ to $z>3$.
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