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To date, more than 500 quasars at z>5 have been discovered. Theoretical models have predicted a high lensed fraction (~4%-20%) for z>5 quasars due to a strong magnification bias. However, only one multiply-imaged quasar at z>5 has been reported (J0439+1634 at z=6.52). We investigate this problem using both analytical models and mock observations. Using updated quasar luminosity functions and deflector velocity dispersion functions, our model suggests we can identify ~10 lensed quasars at z>5 in current imaging surveys. LSST will boost this number to ~45. Simulated observations show that previous high-redshift quasar surveys are highly incomplete for lensed ones. We are carrying out a new survey for high-redshift lensed quasars, with a candidate selection method designed specifically for these objects. So far, we have discovered two strongly-magnified quasars at z>5. Lensing magnification allows us to probe the quasar host galaxies with unprecedented high spatial resolution. Finally, we present the bonus science of our survey -- the discovery of high-redshift close quasar pairs. We are building the first sample of kpc-scale quasar pairs at z>5, which provides unique constraints on the evolution of SMBHs in the early universe.