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We use the very deep and homogeneous I-band selected dataset of the FORS DeepField (FDF) to trace the evolution of the luminosity function over the redshiftrange 0.5 < z < 5.0. We show that the FDF I-band selection down to I(AB)=26.8misses of the order of 10 % of the galaxies that would be detected in a K-bandselected survey with magnitude limit K(AB)=26.3 (like FIRES). Photometricredshifts for 5558 galaxies are estimated based on the photometry in 9 filters(U, B, Gunn g, R, I, SDSS z, J, K and a special filter centered at 834 nm). Acomparison with 362 spectroscopic redshifts shows that the achieved accuracy ofthe photometric redshifts is (Delta z / (z_spec+1)) < 0.03 with only ~ 1 %outliers. This allows us to derive luminosity functions with a reliabilitysimilar to spectroscopic surveys. In addition, the luminosity functions can betraced to objects of lower luminosity which generally are not accessible tospectroscopy. We investigate the evolution of the luminosity functionsevaluated in the restframe UV (1500 Angstroem and 2800 Angstroem), u', B, andg' bands. Comparison with results from the literature shows the reliability ofthe derived luminosity functions. Out to redshifts of z ~ 2.5 the data areconsistent with a slope of the luminosity function approximately constant withredshift, at a value of -1.07 +- 0.04 in the UV (1500 Angstroem, 2800Angstroem) as well as u', and -1.25 +- 0.03 in the blue (g', B). We do not seeevidence for a very steep slope (alpha < -1.6) in the UV at z ~ 3.0 and z ~ 4.0favoured by other authors. There may be a tendency for the faint-end slope tobecome shallower with increasing redshift but the effect is marginal. We find abrightening of M_star and a decrease of Phi_star with redshift for all analyzedwavelengths. [abridged]

The evolution of the luminosity functions in the FORS Deep Field from low to high redshift