The chemical composition of multiple populations in the massive globular cluster (GC) NGC 2808 is addressed with the homogeneous abundance reanalysis of 140 red giant branch stars. UVES spectra for 31 stars and GIRAFFE spectra for the other giants were analyzed with the same procedures used for about 2500 giants in 23 GCs in our FLAMES survey, deriving abundances of Fe, O, Na, Mg, Si, Ca, Ti, Sc, Cr, Mn, and Ni. Iron, elements from {alpha} capture, and those in the Fe group do not show intrinsic scatter. On our UVES scale, the metallicity of NGC 2808 is [Fe/H]=-1.29+/-0.005+/-0.034 (+/-statistical+/-systematic error) with {sigma}=0.030 (31 stars). The main features related to proton-capture elements are retrieved, but the improved statistics and the smaller associated internal errors allow us to uncover five distinct groups of stars along the Na-O anticorrelation. We observe large depletions in Mg, anticorrelated with enhancements of Na and also Si, suggestive of unusually high temperatures for proton captures. About 14% of our sample is formed by giants with solar or subsolar [Mg/Fe] ratios. Using the [Na/Mg] ratios, we confirm the presence of five populations with different chemical compositions that we call P1, P2, I1, I2, and E in order of decreasing Mg and increasing Na abundances. Statistical tests show that the mean ratios in any pair of groups cannot be extracted from the same parent distribution. The overlap with the five populations recently detected from UV photometry is good but not perfect, confirming that more distinct components probably exist in this complex GC.