We present the discovery of three z>5 quasars in the AGN and GalaxyEvolution Survey spectroscopic observations of the NOAO Deep Wide-FieldSurvey (NDWFS) Bootes Field. These quasars were selected as part of alarger Spitzer mid-infrared quasar sample, with no selection based onoptical colors. The highest redshift object, NDWFS J142516.3+325409, atz=5.85, is the lowest luminosity z>5.8 quasar currently known. Wecompare mid-infrared techniques for identifying z>5 quasars to moretraditional optical techniques and show that mid-infrared colors allowfor the selection of high-redshift quasars even at redshifts at whichquasars lie near the optical stellar locus and at z>7, where opticalselection is impossible. Using the superb multiwavelength coverageavailable in the NDWFS Bootes field, we construct the spectral energydistributions (SEDs) of high-redshift quasars from observedBW band to 24 μm (rest-frame 600 Å-3.7 μm). Weshow that the three high-redshift quasars have quite similar SEDs, andthe rest-frame composite SED of low-redshift quasars from the literatureshows little evolution compared to our high-redshift objects. We comparethe number of z>5 quasars we have discovered to the expected numberfrom published quasar luminosity functions. While analyses of the quasarluminosity function are tenuous based on only three objects, we findthat a relatively steep luminosity function with Ψ~L-3.2provides the best agreement with the number of high-redshift quasarsdiscovered in our survey.