  Photonic moir\'e superlattice as an emerging platform of flatbands can
tightly confine the light inside the cavity and has important applications not
only in linear optics but also in nonlinear optics. In this paper, we
numerically investigate the third- and fifth-order harmonic generation (THG and
FHG) in photonic moir\'e superlattices fabricated by the nonlinear material
silicon. The high conversion efficiency of THG and FHG is obtained at a
relatively low intensity of fundamental light, e.g., the maximum conversion
efficiency of THG and FHG arrives even up to be $10^{-2}$ and $10^{-9}$ at the
fundamental intensity of 30 kW/m2, respectively, in the moir\'e superlattice of
near flat band formed by the twist angle 6.01o. The results indicate the
photonic moir\'e superlattice of a high-quality factor and flatbands is a
promising platform for efficient nonlinear processes and advanced photonic
devices.
