  We present the escape fraction of hydrogen ionizing photons (f_esc) from a
sample of 34 high-resolution cosmological zoom-in simulations of galaxies at
z>5 in the Feedback in Realistic Environments project, post-processed with a
Monte Carlo radiative transfer code for ionizing radiation. Our sample consists
of 8500 halos in M_vir~10^8--10^{12} M_sun (M_star~10^4--10^{10} M_sun) at
z=5--12. We find the sample average <f_esc> increases with halo mass for
M_vir~10^8--10^{9.5} M_sun, becomes nearly constant for M_vir~10^{9.5}--10^{11}
M_sun, and decreases at M_vir>10^{11} M_sun. Equivalently, <f_esc> increases
with stellar mass up to M_star~10^8 M_sun and decreases at higher masses. Even
applying single-star stellar population synthesis models, we find a moderate
<f_esc>~0.2 for galaxies at M_star~10^8 M_sun. Nearly half of the escaped
ionizing photons come from stars 1--3 Myr old and the rest from stars 3--10 Myr
old. Binaries only have a modest effect, boosting <f_esc> by ~25--35% and the
number of escaped photons by 60--80%. Most leaked ionizing photons are from
vigorously star-forming regions that usually contain a feedback-driven
kpc-scale superbubble surrounded by a dense shell. The shell is forming stars
while accelerated, so new stars formed earlier in the shell are already inside
the shell. Young stars in the bubble and near the edge of the shell can fully
ionize some low-column-density paths pre-cleared by feedback, allowing a large
fraction of their ionizing photons to escape. The decrease of <f_esc> at the
high-mass end is due to dust attenuation, while at the low-mass end, <f_esc>
decreases owing to inefficient star formation (and hence feedback). At fixed
mass, <f_esc> tends to increase with redshift. Our simulations produce
sufficient ionizing photons for cosmic reionization.
