  We present Atacama Large Millimeter/submillimeter Array observations of the
[C II] 158 $\mu$m line and the underlying continuum emission of TN
J0924$-$2201, which is one of the most distant known radio galaxies at $z>5$.
The [C II] line and 1-mm continuum emission are detected at the host galaxy.
The systemic redshift derived from the [C II] line is $z_{\rm [C
II]}=5.1736\pm0.0002$, indicating that the Ly$\alpha$ line is redshifted by a
velocity of $1035\pm10$ km s$^{-1}$, marking the largest velocity offset
between the [C II] and Ly$\alpha$ lines recorded at $z>5$ to date. In the
central region of the host galaxy, we identified a redshifted substructure of
[C II] with a velocity of $702\pm17$ km s$^{-1}$, which is close to the CIV
line with a velocity of $500\pm10$ km s$^{-1}$. The position and the velocity
offsets align with a model of an outflowing shell structure, consistent with
the large velocity offset of Ly$\alpha$. The non-detection of [C II] and dust
emission from the three CO(1--0)-detected companions indicates their different
nature compared to dwarf galaxies based on the photodissociation region model.
Given their large velocity of $\sim1500$ km s$^{-1}$, outflowing molecular
clouds induced by the AGN is the most plausible interpretation, and they may
exceed the escape velocity of a $10^{13}\,M_{\odot}$ halo. These results
suggest that TN J0924$-$2201, with the ongoing and fossil large-scale outflows,
is in a distinctive phase of removing molecular gas from a central massive
galaxy in an overdense region in the early universe. A dusty HI absorber at the
host galaxy is an alternative interpretation.
