A survey of luminous high-redshift quasars with SDSS and WISE II. the
  bright end of the quasar luminosity function at z ~ 5
  This is the second paper in a series on a new luminous z ~ 5 quasar survey
using optical and near-infrared colors. Here we present a new determination of
the bright end of the quasar luminosity function (QLF) at z ~ 5. Combined our
45 new quasars with previously known quasars that satisfy our selections, we
construct the largest uniform luminous z ~ 5 quasar sample to date, with 99
quasars in the range 4.7 <= z < 5.4 and -29 < M1450 <= -26.8, within the Sloan
Digital Sky Survey (SDSS) footprint. We use a modified 1/Va method including
flux limit correction to derive a binned QLF, and we model the parametric QLF
using maximum likelihood estimation. With the faint-end slope of the QLF fixed
as alpha = -2.03 from previous deeper samples, the best fit of our QLF gives a
flatter bright end slope beta = -3.58+/-0.24 and a fainter break magnitude
M*1450 = -26.98+/-0.23 than previous studies at similar redshift. Combined with
previous work at lower and higher redshifts, our result is consistent with a
luminosity evolution and density evolution (LEDE) model. Using the best fit
QLF, the contribution of quasars to the ionizing background at z ~ 5 is found
to be 18% - 45% with a clumping factor C of 2 - 5. Our sample suggests an
evolution of radio loud fraction with optical luminosity but no obvious
evolution with redshift.
