We present a Fourier analysis of the clustering of galaxies in the combined main galaxy and LRG SDSS DR5 sample. The aim of our analysis is to consider how well we can measure the cosmological matter density using the signature of the horizon at matter-radiation equality embedded in the large-scale power spectrum. The new data constrain the power spectrum on scales 100-600 h-1 Mpc with significantly higher precision than previous analyses of just the SDSS main galaxies, due to our larger sample and the inclusion of the LRGs. This improvement means that we can now reveal a discrepancy between the shape of the measured power and linear CDM models on scales 0.01 h Mpc-1 < k < 0.15 h Mpc-1, with linear model fits favoring a lower matter density (ΩM = 0.22 ± 0.04) on scales 0.01 h Mpc-1 < k < 0.06 h Mpc-1 and a higher matter density (ΩM = 0.32 ± 0.01) when smaller scales are included, assuming a flat ΛCDM model with h = 0.73 and ns = 0.96. This discrepancy could be explained by scale-dependent bias, and by analyzing subsamples of galaxies, we find that the ratio of small-scale to large-scale power increases with galaxy luminosity, so all of the SDSS galaxies cannot trace the same power spectrum shape over 0.01 h Mpc-1 < k < 0.2 h Mpc-1. However, the data are insufficient to clearly show a luminosity-dependent change in the largest scale at which a significant increase in clustering is observed, although they do not rule out such an effect. Significant scale-dependent galaxy bias on large scales, which changes with the r-band luminosity of the galaxies, could potentially explain differences in our ΩM estimates and differences previously observed between 2dFGRS and SDSS power spectra and the resulting parameter constraints.