We present the discovery of a large-scale structure of emission-line galaxies at redshift z=4.86 behind a massive cluster of galaxies, A1689. Previous spectroscopic observations of a galaxy, A1689-7.1 at z=4.87, near this structure, revealed a possible overdense region of intergalactic medium (IGM) around the galaxy, which extends at least ~80 comoving Mpc along the line of sight. In order to investigate whether this z~5 IGM overdense region contains a galaxy overdensity, we undertook narrow- and broad-band imaging observations around A1689-7.1 with Subaru/Suprime-Cam. We detected 51 candidates as Ly{alpha} emitters at redshift z=4.86+/-0.03 in the 32x24-arcmin^2^ field of view. After correction for lensing by the foreground cluster, we found a large-scale (~20x60 comoving Mpc) overdense region of galaxies around A1689-7.1 in the source plane at z=4.86. The densest peak in this region has an overdensity of {delta}~4, suggesting that this structure is probably a good candidate for a protocluster which may evolve into a massive cluster of galaxies in the present-day Universe. A1689-7.1 is located at the edge of this region, where the local galaxy density is ~1.6 times the mean density and is close to the density contrast in the IGM along the line of sight to A1689-7.1 estimated from the optical depth. The overdensities of galaxies we have found may suggest that at least some parts of the IGM overdense region have already started to form galaxies and moreover they relate to the formation of a protocluster. Although we lack information on the three-dimensional distributions of both IGM and galaxy overdense regions, the similarity of the scales of both regions may suggest that the two are parts of a single large-scale structure, which would be an large edge-on sheet along the line of sight with a size of ~20x60x80 comoving Mpc.