  The QSO luminosity function at z>5 provides strong constraints on models of
joint evolution of QSO and their hosts. However, these observations are
challenging because the low space densities of these objects necessitate
surveying of large areas, in order to obtain statistically meaningful samples,
while at the same time cosmological redshifting and dimming means that rather
deep Near Infrared (NIR) imaging must be carried out. Several upcoming and
proposed facilities with wide-field NIR imaging capabilities will open up this
new region of parameter space. In this paper we present predictions for the
expected number counts of z>5 QSOs, based on simple empirical and
semi-empirical models of QSO evolution, as a function of redshift, depth and
surveyed area. We compute the evolution of observed-frame QSO magnitudes and
colors in a representative photometric system covering the wavelength range
550nm<lambda<1800nm, and combine this information with different estimates for
the evolution of the QSO luminosity function. We conclude that planned
ground-based surveys such as Pan-STARRS and VISTA should be able to detect a
large number of luminous QSOs up to z<7.5, but that space-based missions such
as EUCLID (formerly SPACE/DUNE) or SNAP are probably required in order to
obtain substantial samples at higher redshift. We also use our models to
predict the expected number counts for future X-ray space missions (such as
XEUS and Constellation-X), and show that because of their small field-of-view,
these telescopes are unlikely to discover significant numbers of AGN at very
high redshift. However, X-ray follow-up of objects detected at longer
wavelength will be an important means of confirming their identity as AGN and
constraining obscuration.
