  We have used deep Optical Gravitational Lensing Experiment (OGLE-IV) images
($V \lesssim 23$ mag, $I \lesssim 23$ mag at $3\sigma$) of the Magellanic
System, encompassing an area of $\sim$670 deg$^2$, to perform a search for
high-$z$ quasar candidates. We combined the optical OGLE data with the mid-IR
Wide-field Infrared Survey Explorer (WISE) 3.4/4.6/12 $\mu$m data, and devised
a multi-color selection procedure. We have identified 33 promising sources and
then spectroscopically observed the two most variable ones. We report the
discovery of two high-$z$ quasars, OGLE J015531-752807 at a redshift $z=5.09$
and OGLE J005907-645016 at a redshift of $z=4.98$. The variability amplitude of
both quasars at the rest-frame wavelength $\sim$1300\AA\ is much larger
($\sim$0.4 mag) than other quasars ($<0.15$ mag) at the same rest-frame
wavelength but lower redshifts ($2<z<4$). To verify if there exist an increased
variability amplitude in high-$z$ population of quasars, simply a larger sample
of such sources with a decade long (or longer) light curves is necessary, which
will be enabled by the Large Synoptic Survey Telescope (LSST) providing light
curves for sources 3-4 mag fainter than OGLE.
