Combining high time and frequency resolution full-polarisation spectra of Fast Radio Bursts (FRBs) with knowledge of their host galaxy properties provides an opportunity to study both the emission mechanism generating them and the impact of their propagation through their local environment, host galaxy, and the intergalactic medium. The Australian Square Kilometre Array Pathfinder (ASKAP) telescope has provided the first ensemble of bursts with this information. In this paper, we present the high time and spectral resolution, full polarisation observations of five localised FRBs to complement the results published for the previously studied ASKAP FRB~181112. We find that every FRB is highly polarised, with polarisation fractions ranging from 80 -- 100%, and that they are generally dominated by linear polarisation. While some FRBs in our sample exhibit properties associated with an emerging archetype (i.e., repeating or apparently non-repeating), others exhibit characteristic features of both, implying the existence of a continuum of FRB properties. When examined at high time resolution, we find that all FRBs in our sample have evidence for multiple sub-components and for scattering at a level greater than expected from the Milky Way. We find no correlation between the diverse range of FRB properties (e.g., scattering time, intrinsic width, and rotation measure) and any global property of their host galaxy. The most heavily scattered bursts reside in the outskirts of their host galaxies, suggesting that the source-local environment rather than the host interstellar medium is likely the dominant origin of the scattering in our sample.
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