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We present a new catalogue of radio sources in the face-on spiral galaxy M83. Radio observations taken in 2011, 2015, and 2017 with the Australia Telescope Compact Array (ATCA) at 5.5 and 9 GHz have detected 270 radio sources. Although a small number of these sources are background extragalactic sources, most are either H II regions or supernova remnants (SNRs) within M83 itself. Three of the six historical supernovae are detected, as is the very young remnant that had been identified in a recent study, which is likely the result of a supernova that exploded in the last ~100 years but was missed. All of these objects are generally fading with time. Confusion limits our ability to measure the radio emission from a number of the SNRs in M83, but 64 were detected in unconfused regions, and these have the approximate power-law luminosity function which has been observed in other galaxies. The SNRs in M83 are systematically smaller in diameter and brighter than those that have been detected at radio wavelengths in M33. A number of the radio sources are coincident with X-ray sources in M83; most of these coincident sources turn out to be supernova remnants. Our dual frequency observations are among the most sensitive to date for a spiral galaxy outside the Local Group; despite this we were not able to place realistic constraints on the spectral indices, and as a result, it was not possible to search for supernova remnants based on their radio properties alone.