We present Atacama Large Millimeter/submillimeter Array observations of the [C II] 158 μm 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[C II]=5.1736±0.0002, indicating that the Lyα line is redshifted by a velocity of 1035±10 km s⁻¹, marking the largest velocity offset between the [C II] and Lyα 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±17 km s⁻¹, which is close to the CIV line with a velocity of 500±10 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 Lyα. 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 ~1500 km s⁻¹, outflowing molecular clouds induced by the AGN is the most plausible interpretation, and they may exceed the escape velocity of a 10¹³\,M_ 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.
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