  We investigate the luminosity functions of Lyman-break galaxies (LBG) at z~4
and 5 based on the optical imaging data obtained in the Subaru Deep Field
Project. Three samples of LBGs in a contiguous 875 arcmin^2 area are
constructed. One consists of 3,808 LBGs at z~4 down to i'=26.85 selected with
the B-R vs R-i' diagram. The other two consist of 539 and 240 LBGs at z~5 down
to z'=26.05 selected with two kinds of two-color diagrams: V-i' vs i'-z' and
R-i' vs i'-z'. The adopted selection criteria are proved to be fairly reliable
by spectroscopic observation. We derive the luminosity functions of the LBGs at
rest-frame ultraviolet wavelengths down to M_{UV}=-19.2 at z~4 and M_{UV}=-20.3
at z~5. We find clear evolution of the luminosity function over the redshift
range of 0<z<6, which is accounted for by a sole change in the characteristic
magnitude, M^*. The cosmic star formation rate (SFR) density at z~4 and z~5 is
measured from the luminosity functions. We examine the evolution of the cosmic
SFR density and its luminosity dependence over 0<z<6. The SFR density
contributed from brighter galaxies is found to change more drastically with
cosmic time. The contribution from brighter galaxies has a sharp peak around
z=3-4, while that from fainter galaxies evolves relatively mildly with a broad
peak at earlier epoch. Combining the observed SFR density with the standard
Cold Dark Matter model, we compute the cosmic SFR per unit baryon mass in dark
haloes, i.e., the specific SFR. The specific SFR is found to scale with
redshift as (1+z)^3 up to z~4, implying that the efficiency of star formation
is on average higher at higher redshift in proportion to the cooling rate
within dark haloes, while this is not simply the case at z>4.
