We have obtained spectroscopic observations from 3600 Åto 9200 Åwith FORS at the Very Large Telescope for approximately 70 H iiregions located in the spiral galaxies NGC 1232, NGC 1365, NGC 2903, NGC 2997 and NGC 5236. These data are part of a project to measure the chemical abundances and characterize the massive stellar content of metal-rich extragalactic H iiregions. In this paper we describe our dataset, and present emission line fluxes for the whole sample. In 32 H iiregions we measure at least one of the following auroral lines: [S ii]4072, [N ii]5755, [S iii]6312 and [O ii]7325. From these we derive electron temperatures, as well as oxygen, nitrogen and sulphur abundances, using classical empirical methods (both so-called “T_e-based methods” and “strong line methods”). Under the assumption that the temperature does not introduce severe biases, we find that the most metal-rich nebulae with detected auroral lines are found at 12 + log(O/H)  8.9, i.e. about 60% larger than the adopted solar value. However, classical abundance determinations in metal-rich H iiregions may be severely biased and must be tested with realistic photoionization models. The spectroscopic observations presented in this paper will serve as a homogeneous and high-quality database for such purposes.