  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 $3<z\lesssim5$ 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 $\mathrm{logL_X\sim43-45}$ 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 $0.54\pm0.05$,
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 $z>3$.
