We report the results of a programme of dual-epoch Chandra ACIS-S observations of five ultraluminous X-ray sources (ULXs) in nearby spiral galaxies. All five ULXs are detected as unresolved, point-like X-ray sources by Chandra, though two have faded below the 10^39 erg/s luminosity threshold used to first designate these sources as ULXs. Using this same criterion, we detect three further ULXs within the imaged regions of the galaxies. The ULXs appear to be related to the star forming regions of the galaxies, indicating that even in ``normal spiral galaxies the ULX population is predominantly associated with young stellar populations. A detailed study of the Chandra ACIS-S spectra of six of the ULXs shows that five are better described by a powerlaw continuum than a multi-colour disc blackbody model, though there is evidence for additional very soft components to two of the powerlaw continua. The measured photon indices in four out of five cases are consistent with the low/hard state in black hole binaries, contrary to the suggestion that powerlaw-dominated spectra of ULXs originate in the very high state. A simple interpretation of this is that we are observing accretion onto intermediate-mass black holes, though we might also be observing a spectral state unique to very high mass accretion rates in stellar-mass black hole systems. Short-term flux variability is only detected in one of two epochs for two of the ULXs, with the lack of this characteristic arguing that the X-ray emission of this sample of ULXs is not dominated by relativistically-beamed jets. The observational characteristics of this small sample suggest that ULXs are a distinctly heterogeneous source class.
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