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We present a detailed study of the strengths of the calcium triplet absorption lines in the spectra of a large sample of red giant members of the luminous outer Galactic halo globular cluster NGC 5824. The spectra were obtained with the FORS2 and GMOS-S multi-object spectrographs at the VLT and the Gemini-S telescope, respectively. By comparing the line strengths of the NGC 5824 stars with those for red giants in clusters with well-established abundances, we conclude that there is an intrinsic abundance dispersion in NGC 5824 characterized by an inter-quartile range in [Fe/H] of 0.10dex and a total range of ∼ 0.3dex. As for ω Cen and M22, the abundance distribution shows a steep rise on the metal-poor side and a shallower decline on the metal-rich side. There is also some indication that the distribution is not unimodal with perhaps three distinct abundance groupings present. NGC 5824 has a further unusual characteristic: the outer surface density profile shows no signs of a tidal cutoff. Instead, the profile has a power-law distribution with cluster stars detected to a radius exceeding 400 pc. We postulate that NGC 5824 may be the remnant nuclear star cluster of a now disrupted dwarf galaxy accreted during the formation of the Galaxy's halo. We further speculate that the presence of an intrinsic [Fe/H] spread is the characteristic that distinguishes former nuclear star clusters from other globular clusters.