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We present the results from the search for Lyman Alpha emitters (LAEs) in the proximity of 11 civ absorption systems at $z>4.7$ in the spectrum of the QSO J1030+0524, using data from MUSE.We have found multiple LAE candidates close to four civ systems at $z_{ext{civ}}=4.94$--5.74 with $log_{10}(N_{ext{civ}}[$cm$])>13.5$. At $z=5$--6, civ systems with W$_0(ext{civ})> 0.2$ AA seem more likely to have galaxies with Lya emission within $ho< 200$ proper kpc (4/5 cases), than the civ systems with W$_0(ext{civ}) 0.5$ AA is in the range $11, simlt,ho,simlt,200$ proper kpc (pkpc). Furthermore, all candidates are in the luminosity range0.18--1.15 L$^{star}_{ext{Lya}}(z=5.7)$, indicating that the environment of civ systems within 200 pkpc is populated by the faint end of the Lya luminosity function. We report a 0.28,L$^{star}_{ext{Lya}}$ galaxy at a separation of $ho=11$ pkpc from a strong civ absorption ($log_{10}(N_{ext{civ}}[$cm$])=14.52$) at $z_{ext{civ}}=5.72419$. The prevalence of sub-L$^{star}_{ext{Lya}}$ galaxies in the proximity of $z>4.9$ civ systemssuggest that the absorbing material is rather young, likely ejected in the recent past of the identified galaxies. The connection between faint LAEs and high-ionization absorption systems reported in this work, is potentially a consequence of the role of low mass galaxies in the early evolution of the circum-galactic and intergalactic media.