Context : Aims : We obtained VLT/FLAMES+UVES high-resolution , fibre-fed spectroscopy of five young massive clusters ( YMCs ) in M83 ( NGC 5236 ) . This forms the basis of a pilot study testing the feasibility of using fibre-fed spectroscopy to measure the velocity dispersions of several clusters simultaneously , in order to determine their dynamical masses . In principle , this reduces the telescope time required to obtain a statistically significant sample of dynamical cluster masses . These can be used to assess the long-term survivability of YMCs by comparing their dynamical and photometric masses , which are necessary to ascertain the potential evolution of YMCs into second-generation globular clusters . Methods : We adopted two methods for determining the velocity dispersion of the star clusters : cross-correlating the cluster spectrum with the template spectra and minimising a \chi ^ { 2 } value between the cluster spectrum and the broadened template spectra . We also considered both red giant and red supergiant template stars . Cluster 805 in M83 ( following the notation of Larsen ) was chosen as a control to test the reliability of the results obtained by this observational method , through a comparison with the results obtained from a standard echelle VLT/UVES spectrum obtained by Larsen & Richtler . Results : We find no dependence of the velocity dispersions measured for a cluster on the choice of red giant versus red supergiant templates , nor on the method adopted . However , we do find that the standard deviation of the results obtained with only one method may underestimate the true uncertainty . We measure a velocity dispersion of \sigma _ { \mathrm { los } } = 10.2 \pm 1.1 \mathrm { km s } ^ { -1 } for cluster 805 from our fibre-fed spectroscopy . This is in excellent agreement with the velocity dispersion of \sigma _ { \mathrm { los } } = 10.6 \pm 1.4 \mathrm { km s } ^ { -1 } determined from the standard echelle UVES spectrum of cluster 805 . Our FLAMES+UVES velocity dispersion measurement gives M _ { \mathrm { vir } } = ( 6.6 \pm 1.7 ) \times 10 ^ { 5 } M _ { \odot } , consistent with previous results . This value of the virial mass is a factor of \sim 3 greater than the cluster ’ s photometric mass , indicating a lack of virial equilibrium . However , based on its effective star formation efficiency , the cluster is likely to virialise , and may survive for a Hubble time , in the absence of external disruptive forces . Unfortunately , our observations of the other M83 star clusters have insufficient signal-to-noise ratios to determine robust cluster velocity dispersions . Conclusions : We find that reliable velocity dispersions can be determined from high-resolution , fibre-fed spectroscopy . The advantages of observing several clusters simultaneously outweighs the difficulty of accurate galaxy background subtraction , providing that the targets are chosen to provide sufficient signal-to-noise ratios , and are much brighter than the galaxy background .