  Active galactic nuclei (AGNs) in the high-redshift Universe are thought to
reside in overdense environments. However, recent works provide controversial
results partly due to the use of different techniques and possible suppression
of nearby galaxy formation by AGN feedback. We conducted deep and wide-field
imaging observations with the Suprime-Cam on the Subaru telescope and searched
for Lyman-alpha emitters (LAEs) around two QSOs (quasi-stellar objects) at
$z\sim4.9$ and a radio galaxy at $z\sim4.5$ by using narrow-band filters to
address these issues more robustly. In the QSO fields, we obtained additional
broad-band images to select Lyman-break galaxies (LBGs) at $z\sim5$ for
comparison. We constructed a photometric sample of 301 LAEs and 170 LBGs in
total. A wide field of view (34arcmin$\times$27arcmin, corresponding to
80$\times$60 comoving Mpc$^2$) of the Suprime-Cam enabled us to probe galaxies
in the immediate vicinities of the AGNs and in the blank fields simultaneously
and compare various properties of them in a consistent manner. The two QSOs are
located near local density peaks ($<2\sigma$) and one of the QSOs has a close
companion LAE with projected separation of 80 physical kpc. The radio galaxy is
found to be near a void of LAEs. The number densities of LAEs/LGBs in a larger
spatial scale around the AGNs are not significantly different from those in
blank fields. No sign of feedback is found down to
$L_{Ly\alpha}\sim10^{41.8}\mathrm{~erg~s^{-1}}$. Our results suggest that
high-redshift AGNs are not associated with extreme galaxy overdensity and that
this cannot be attributed to the effect of AGN feedback.
