  We present the discovery of three z>5 quasars in the AGN and Galaxy Evolution
Survey (AGES) spectroscopic observations of the NOAO Deep Wide-Field Survey
(NDWFS) Bootes Field. These quasars were selected as part of a larger Spitzer
mid-infrared quasar sample with no selection based on optical colors. The
highest redshift object, NDWFS J142516.3+325409, z=5.85, is the
lowest-luminosity z>5.8 quasar currently known. We compare mid-infrared
techniques for identifying z>5 quasars to more traditional optical techniques
and show that mid-infrared colors allow for selection of high-redshift quasars
even at redshifts where quasars lie near the optical stellar locus and at z>7
where optical selection is impossible. Using the superb multi-wavelength
coverage available in the NDWFS Bootes field, we construct the spectral energy
distributions (SEDs) of high-redshift quasars from observed Bw-band to 24
microns (rest-frame 600 Angstroms - 3.7 microns). We show that the three
high-redshift quasars have quite similar SEDs, and the rest-frame composite SED
of low-redshift quasars from the literature shows little evolution compared to
our high-redshift objects. We compare the number of z>5 quasars we have
discovered to the expected number from published quasar luminosity functions.
While analyses of the quasar luminosity function are tenuous based on only
three objects, we find that a relatively steep luminosity function with Psi
L^(-3.2) provides the best agreement with the number of high-redshift quasars
discovered in our survey.
