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We report the first results of a high-redshift ($z$ >~ 5) quasar survey usingthe Dark Energy Spectroscopic Instrument (DESI). As a DESI secondary targetprogram, this survey is designed to carry out a systematic search andinvestigation of quasars at $z$ >~ 5, up to redshift 6.8. The target selectionis based on the DESI Legacy Imaging Surveys (the Legacy Surveys) DR9photometry, combined with the Pan-STARRS1 data and $J$-band photometry frompublic surveys. A first quasar sample has been constructed from the DESI SurveyValidation 3 (SV3) and first-year observations until May 2022. This sampleincludes more than 400 new quasars at redshift 4.7 <= $z$ < 6.6, down to 21.5magnitude in the $z$ band, discovered from 35% of the entire target sample.Remarkably, there are 220 new quasars identified at $z$ >= 5, more than onethird of existing quasars previously published at this redshift. Theobservations so far result in an average success rate of 23% at $z$ > 4.7. Thecurrent spectral dataset has already allowed analysis of interesting individualobjects (e.g., quasars with damped Ly$\alpha$ absorbers and broad absorptionline features), and statistical analysis will follow the survey's completion. Aset of science projects will be carried out leveraging this program, includingquasar luminosity function, quasar clustering, intergalactic medium, quasarspectral properties, intervening absorbers, and properties of earlysupermassive black holes. Additionally, a sample of 38 new quasars at $z$ ~3.8-5.7 discovered from a pilot survey in the DESI SV1 is also published inthis paper.

DESI z >~ 5 Quasar Survey. I. A First Sample of 400 New Quasars at z ~ 4.7-6.6