We analyze five years of PLANET photometry of microlensing events toward the Galactic bulge to search for the short-duration deviations from single lens light curves that are indicative of the presence of planetary companions to the primary microlenses . Using strict event selection criteria , we construct a well defined sample of 43 intensively monitored events . We search for planetary perturbations in these events over a densely sampled region of parameter space spanning two decades in mass ratio and projected separation , but find no viable planetary candidates . By combining the detection efficiencies of the events , we find that , at 95 % confidence , less than 25 \% of our primary lenses have companions with mass ratio q = 10 ^ { -2 } and separations in the lensing zone , [ 0.6 - 1.6 ] \theta _ { E } , where \theta _ { E } is the Einstein ring radius . Using a model of the mass , velocity and spatial distribution of bulge lenses , we infer that the majority of our lenses are likely M dwarfs in the Galactic bulge . We conclude that < 33 \% of M-dwarfs in the Galactic bulge have companions with mass m _ { p } = M _ { Jup } between 1.5 and 4 ~ { } { AU } , and < 45 \% have companions with m _ { p } = 3 M _ { Jup } between 1 and 7 ~ { } { AU } , the first significant limits on planetary companions to M-dwarfs . We consider the effects of the finite size of the source stars and changing our detection criterion , but find that these do not alter our conclusions substantially .