  We measure and study the evolution of the UV galaxy Luminosity Function (LF)
at z=3-5 from the largest high-redshift survey to date, the Deep part of the
CFHT Legacy Survey. We also give accurate estimates of the SFR density at these
redshifts. We consider ~100,000 Lyman-break galaxies at z~3.1, 3.8 & 4.8
selected from very deep ugriz images of this data set and estimate their
rest-frame 1600A luminosity function. Due to the large survey volume, cosmic
variance plays a negligible role. Furthermore, we measure the bright end of the
LF with unprecedented statistical accuracy. Contamination fractions from stars
and low-z galaxy interlopers are estimated from simulations. To correct for
incompleteness, we study the detection rate of simulated galaxies injected to
the images as a function of magnitude and redshift. We estimate the
contribution of several systematic effects in the analysis to test the
robustness of our results. We find the bright end of the LF of our u-dropout
sample to deviate significantly from a Schechter function. If we modify the
function by a recently proposed magnification model, the fit improves. For the
first time in an LBG sample, we can measure down to the density regime where
magnification affects the shape of the observed LF because of the very bright
and rare galaxies we are able to probe with this data set. We find an increase
in the normalisation, $\phi^{*}$, of the LF by a factor of 2.5 between z~5 and
z~3. The faint-end slope of the LF does not evolve significantly between z~5
and z~3. We do not find a significant evolution of the characteristic magnitude
in the studied redshift interval. The SFR density is found to increase by a
factor of ~2 from z~5 to z~4. The evolution from z~4 to z~3 is less eminent.
