  The launch of ${\it JWST}$ opens a new window for studying the connection
between metal-line absorbers and galaxies at the end of the Epoch of
Reionization (EoR). Previous studies have detected absorber-galaxy pairs in
limited quantities through ground-based observations. To enhance our
understanding of the relationship between absorbers and their host galaxies at
$z>5$, we utilized the NIRCam Wide Field Slitless Spectroscopy (WFSS) to search
for absorber-associated galaxies by detecting their rest-frame optical emission
lines (e.g., [OIII] + H$\beta$). We report the discovery of a MgII-associated
galaxy at $z=5.428$ using data from the ${\it JWST}$ ASPIRE program. The MgII
absorber is detected on the spectrum of quasar J0305--3150 with a rest-frame
equivalent width of 0.74$\mathring{A}$. The associated galaxy has an [OIII]
luminosity of $10^{42.5}\ {\rm erg\ s^{-1}}$ with an impact parameter of 24.9
proper kiloparsecs (pkpc). The joint ${\it HST}$-${\it JWST}$ spectral energy
distribution (SED) implies a stellar mass and star-formation rate of ${\rm M_*
\approx 10^{8.8}}$ ${\rm M_{\odot}}$, ${\rm SFR}\approx 10\ {\rm M_{\odot}\
yr^{-1}}$. Its [OIII] equivalent width and stellar mass are typical of [OIII]
emitters at this redshift. Furthermore, connecting the outflow starting time to
the SED-derived stellar age, the outflow velocity of this galaxy is $\sim300\
{\rm km\ s^{-1}}$, consistent with theoretical expectations. We identified six
additional [OIII] emitters with impact parameters of up to $\sim300$ pkpc at
similar redshifts ($|dv|<1000\ {\rm km\ s^{-1}}$). The observed number is
consistent with that in cosmological simulations. This pilot study suggests
that systematically investigating the absorber-galaxy connection within the
ASPIRE program will provide insights into the metal-enrichment history in the
early universe.
