Differential cross sections have been measured for (d, Li7) and [d, Li7*(0.478)] reactions from C13, O17, O18, and F19 as well as for F19(d, Be7), F19[d, Be7*(0.432)], F19(d, Be9)C12, and F19(d, Be9)C12*(4.43), utilizing simultaneous time-of-flight and energy analysis. All 12 angular distributions for these many-nucleon transfer reactions were obtained at incident deuteron energies near 15 MeV, and show forward peaking and noticeable, diffraction-like structure as well as large total cross sections (0.1<σtot<1.8 mb). Hence most (d, Li7) cross sections reported here are comparable in magnitude to those of (d, Li6) reactions from corresponding targets. An interpretation of these many-nucleon transfers in terms of a simple direct-reaction model is attempted. Distorted-wave Born-approximation (DWBA) calculations were made, analogous to earlier calculations for (d, Li6) angular distributions on similar targets. DWBA curves with a damped diffraction structure are obtained easily, since for 5-nucleon transfers, the angular distribution usually has contributions from two different l transfers. Our DWBA calculations for these reactions yield the correct order of magnitude for the absolute total cross sections, and qualitative agreement in the angular distributions. Tentative spectroscopic coefficients are extracted from the comparison of experiment and calculations.