We present the Data Release 4&5 quasar catalog from the quasar survey by Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST), which includes quasars observed between September 2015 and June 2017. There are a total of 19,253 quasars identified by visual inspections of the spectra. Among them, 11,458 are independently discovered by LAMOST, in which 3296 were reported by SDSS DR12 and DR14 quasar catalog after our survey began, while the rest 8162 are new discoveries of LAMOST. We provide the emission line measurements for the Halpha, Hbeta, MgII and/or CIV for 18100 quasars. Since LAMOST does not have absolute flux calibration information, we obtain the monochromatic continuum luminosities by fitting the SDSS photometric data using the quasar spectra, and then estimate the black hole masses. The catalog and spectra for these quasars are available online. This is the third installment in the series of LAMOST quasar survey which has released spectra for totally ~43,000 quasars hitherto. There are 24,772 independently discovered quasars, 17,128 of which are newly discovered. In addition to the great supplement to the new quasar discoveries, LAMOST has also provided a large database (overlapped with SDSS) for investigating the quasar spectral variability and discovering unusual quasars, including changing-look quasars, with ongoing and upcoming large surveys.
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