We here present the luminosity function (LF) of globular clusters (GCs) in five nearby spiral galaxies using the samples of GC candidates selected in Hubble Space Telescope mosaic images in F435W, F555W, and F814W filters. Our search, which surpasses the fractional area covered by all previous searches in these galaxies, has resulted in the detection of 158 GC candidates in M81, 1123 in M101, 226 in NGC 4258, 293 in M51, and 173 in NGC 628. The LFs constructed from this data set, after correcting for relatively small contamination from reddened young clusters, are lognormal in nature, which was hitherto established only for the Milky Way (MW) and Andromeda among spiral galaxies. The magnitude at the turn-over (TO) corresponds to M_V0_(TO)=-7.41+/-0.14 in four of the galaxies with Hubble types Sc or earlier, in excellent agreement with M_V_(TO)=-7.40+/-0.10 for the MW. The TO magnitude is equivalent to a mass of ~3x10^5^M_{sun}_ for an old, metal-poor population. MV0(TO) is fainter by ~1.16 magnitude for the fifth galaxy, M 101, which is of Hubble type Scd. The TO dependence on Hubble type implies that the GCs in early-type spirals are classical GCs, which have a universal TO, whereas the GC population in late-type galaxies is dominated by old disc clusters, which are in general less massive. The radial density distribution of GCs in our sample galaxies follows the Sersic function with exponential power-law indices, and effective radii of 4.0-9.5kpc. GCs in the sample galaxies have a mean specific frequency of 1.10+/-0.24, after correcting for magnitude and radial incompleteness factors.