We present integrated-light (IL) spectra of eight young massive clusters (YMCs) in the metal-rich spiral galaxy NGC 5236 (M83). The observations were taken with the X-Shooter spectrograph on the ESO Very Large Telescope. Through the use of theoretical isochrones and synthetic IL spectra, we derive metallicities and study the radial metallicity gradient observed through these young populations. For the inner regions of the galaxy, we observe a relatively shallow metallicity gradient of -0.37 ± 0.29 dex R_{25}^{-1}, agreeing with chemical evolution models with an absence of infall material and a relatively low mass-loss due to winds in the inner parts of the disc. We estimate a central metallicity of [Z] = +0.17 ± 0.12 dex, finding excellent agreement with that obtained via other methods (e.g. blue supergiants and J band). We infer a metallicity of 12+log(O/H) = 8.75 ± 0.08 dex at R/R25 = 0.4, which fits the stellar mass-metallicity relation compilation of blue supergiants and IL studies.