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We present a measurement of the evolution of the stellar mass function (MF)of galaxies and the evolution of the total stellar mass density at 0<z<5. Weuse deep multicolor data in the Fors Deep Field (FDF; I-selected reachingI_AB=26.8) and the GOODS-S/CDFS region (K-selected reaching K_AB=25.4) toestimate stellar masses based on fits to composite stellar population modelsfor 5557 and 3367 sources, respectively. The MF of objects from the GOODS-Ssample is very similar to that of the FDF. Near-IR selected surveys hencedetect the more massive objects of the same principal population as doI-selected surveys. We find that the most massive galaxies harbor the oldeststellar populations at all redshifts. At low z, our MF follows the local MFvery well, extending the local MF down to 10^8 Msun. The faint end slope isconsistent with the local value of alpha~1.1 at least up to z~1.5. Our MF alsoagrees very well with the MUNICS and K20 results at z<2. The MF seems to evolvein a regular way at least up to z~2 with the normalization decreasing by 50% toz=1 and by 70% to z=2. Objects having M>10^10 Msun which are the likelyprogenitors of todays L* galaxies are found in much smaller numbers above z=2.However, we note that massive galaxies with M>10^11 Msun are present even tothe largest redshift we probe. Beyond z=2 the evolution of the mass functionbecomes more rapid. We find that the total stellar mass density at z=1 is 50%of the local value. At z=2, 25% of the local mass density is assembled, and atz=3 and z=5 we find that at least 15% and 5% of the mass in stars is in place,respectively. The number density of galaxies with M>10^11 Msun evolves verysimilarly to the evolution at lower masses. It decreases by 0.4 dex to z=1, by0.6 dex to z=2, and by 1 dex to z=4.Comment: Accepted for publication in ApJ

The Stellar Mass Function of Galaxies to z ~ 5 in the FORS Deep and GOODS-South Fields