We have obtained spectroscopic observations from 3600{AA} to 9200{AA} with FORS at the Very Large Telescope for approximately 70 HII regions located in the spiral galaxies NGC 1232, NGC 1365, NGC 2903, NGC 2997 and NGC 5236. These data are part of a project aiming at measuring the chemical abundances and characterizing the massive stellar content of metal-rich extragalactic HII regions. In this paper we describe our dataset, and present emission line fluxes for the whole sample. In 32 HII regions 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 "Te-based methods" and "strong line methods"). Under the assumption that the temperature gradient 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 HII regions 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 purpose.