We test the galactic outflow model by probing associated galaxies of four strong intergalactic CIV absorbers at $z=5$--6 using the Hubble Space Telescope (HST) ACS ramp narrowband filters. The four strong CIV absorbers reside at $z=5.74$, $5.52$, $4.95$, and $4.87$, with column densities ranging from $N_{rm{CIV}}=10^{13.8}$ cm$^{-2}$ to $10^{14.8}$ cm$^{-2}$. At $z=5.74$, we detect an i-dropout Ly$alpha$ emitter (LAE) candidate with a projected impact parameter of 42 physical kpc from the CIV absorber. This LAE candidate has a Ly$alpha$-based star formation rate (SFR$_{rm{Lyalpha}}$) of 2 $M_odot$ yr$^{-1}$ and a UV-based SFR of 4 $M_odot$ yr$^{-1}$. Although we cannot completely rule out that this $i$-dropout emitter may be an [OII] interloper, its measured properties are consistent with the CIV powering galaxy at $z=5.74$. For CIV absorbers at $z=4.95$ and $z=4.87$, although we detect two LAE candidates with impact parameters of 160 kpc and 200 kpc, such distances are larger than that predicted from the simulations. Therefore we treat them as non-detections. For the system at $z=5.52$, we do not detect LAE candidates, placing a 3-$sigma$ upper limit of SFR$_{rm{Lyalpha}}approx 1.5 M_odot$ yr$^{-1}$. In summary, in these four cases, we only detect one plausible CIV source at $z=5.74$. Combining the modest SFR of the one detection and the three non-detections, our HST observations strongly support that smaller galaxies (SFR$_{rm{Lyalpha}} lesssim 2 M_odot$ yr$^{-1}$) are main sources of intergalactic CIV absorbers, and such small galaxies play a major role in the metal enrichment of the intergalactic medium at $zgtrsim5$.
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