We present a Fourier analysis of the clustering of galaxies in the combined Main galaxy and Luminous Red Galaxy (LRG) Sloan Digital Sky Survey (SDSS) Data Release 5 (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 constrains the power spectrum on scales 100--600h^-1Mpc with significantly higher precision than

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... 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<k<0.15hMpc^-1, with linear model fits favouring a lower matter density (Omega_m=0.22+/-0.04) on scales 0.01<k<0.06hMpc^-1 and a higher matter density (Omega_m=0.32+/-0.01) when smaller scales are included, assuming a flat LCDM model with h=0.73 and n_s=0.96. This discrepancy could be explained by scale-dependent bias and, by analysing 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<k<0.2hMpc^-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 Omega_m estimates and differences previously observed between 2dFGRS and SDSS power spectra and the resulting parameter constraints.