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We present a study of the structure and local dynamics of dispersed silica nanoparticles in the liquid crystal 4′-pentyl-4-biphenylcarbonitrile (5CB). Electron microscopy and X-ray scattering data demonstrate that the nanoparticles form agglomerates with a fractal structure. Investigation of the local dynamics of the particle agglomerates using X-ray photon correlation spectroscopy reveals pronounced anisotropy in the relaxation rate and aging behaviour. We suggest that the unusual relaxation behaviour is a consequence of the anisotropy of the host solvent.