X-ray observations of quiescent X-ray binaries have the potential to provide insight into the structure and the composition of neutron stars. EXO 0748-676 had been actively accreting for over 24 yr before its outburst ceased in late 2008. Subsequent X-ray monitoring revealed a gradual decay of the quiescent thermal emission that can be attributed to cooling of the accretion-heated neutron star crust. In this work, we report on new Chandra and Swift observations that extend the quiescent monitoring to ~5 yr post-outburst. We find that the neutron star temperature remained at ~117 eV between 2009 and 2011, but had decreased to ~110 eV in 2013. This suggests that the crust has not fully cooled yet, which is supported by the lower temperature of ~95 eV that was measured ~4 yr prior to the accretion phase in 1980. Comparing the data to thermal evolution simulations reveals that the apparent lack of cooling between 2009 and 2011 could possibly be a signature of convection driven by phase separation of light and heavy nuclei in the outer layers of the neutron star.