We present the determination of stellar parameters and individual elemental abundances for 6 million stars from ~8 million low-resolution (R~1800) spectra from LAMOST DR5. This is based on a modeling approach that we dub the data-driven Payne (DD-Payne), which inherits essential ingredients from both the Payne and the Cannon. It is a data-driven model that incorporates constraints from theoretical spectral models to ensure the derived abundance estimates are physically sensible. Stars in LAMOST DR5 that are in common with either GALAH DR2 or APOGEE DR14 are used to train a model that delivers stellar parameters (Teff, log g, Vmic) and abundances for 16 elements (C, N, O, Na, Mg, Al, Si, Ca, Ti, Cr, Mn, Fe, Co, Ni, Cu, and Ba) over a metallicity range of -4dex<[Fe/H]<0.6dex when applied to the LAMOST spectra. Cross-validation and repeat observations suggest that, for S/N_pixel_>=50, the typical internal abundance precision is 0.03-0.1dex for the majority of these elements, with 0.2-0.3dex for Cu and Ba, and the internal precision of Teff and logg is better than 30K and 0.07dex, respectively. Abundance systematics at the ~0.1dex level are present in these estimates but are inherited from the high-resolution surveys' training labels. For some elements, GALAH provides more robust training labels, for others, APOGEE. We provide flags to guide the quality of the label determination and identify binary/multiple stars in LAMOST DR5.