We have performed a spectroscopic study of globular clusters (GCs) in the nearest giant elliptical NGC 5128 using the 2dF facility at the Anglo-Australian Telescope. We obtained integrated optical spectra for a total of 254 GCs, 79 of which are newly confirmed on the basis of their radial velocities and spectra. In addition, we obtained an integrated spectrum of the galaxy starlight along the southern major axis. We derive an empirical metallicity distribution function (MDF) for 207 GCs (~14 per cent of the estimated total GC system) based upon Milky Way GCs. This MDF is multimodal at high statistical significance with peaks at [Z/H] ~ -1.3 and -0.5. A comparison between the GC MDF and that of the stellar halo at 20 kpc (~4Re) reveals close coincidence at the metal-rich ends of the distributions. However, an inner 8-kpc stellar MDF shows a clear excess of metal-rich stars when compared to the GCs. We compare a higher signal-to-noise ratio (S/N) subsample (147 GCs) with two stellar population models which include non-solar abundance ratio corrections. The vast majority of our sample (~90 per cent) appears old, with ages similar to the Milky Way GC system. There is evidence for a population of intermediate-age (~4-8 Gyr) GCs (<=15 per cent of the sample) which are on average more metal-rich than the old GCs. We also identify at least one younger cluster (~1-2 Gyr) in the central regions of the galaxy. Our observations are consistent with a picture where NGC 5128 has undergone at least two mergers and/or interactions involving star formation and limited GC formation since z = 1, however the effect of non-canonical hot stellar populations on the integrated spectra of GCs remains an outstanding uncertainty in our GC age estimates.