Emission from the 6.7 GHz methanol maser transition is very strong, is relatively stable, has small internal motions, and is observed toward numerous massive star-forming regions in the Galaxy. Our goal is to perform high-precision astrometry using this maser transition to obtain accurate distances to their host regions. Eight strong masers were observed during five epochs of VLBI observations with the European VLBI Network between 2006 June, and 2008 March. We report trigonometric parallaxes for five star-forming regions, with accuracies as good as $sim22 mathrm{mu}$as. Distances to these sources are $2.57^{+0.34}_{-0.27}$ kpc for ON 1, $0.776^{+0.104}_{-0.083}$ kpc for L 1206, $0.929^{+0.034}_{-0.033}$ kpc for L 1287, $2.38^{+0.13}_{-0.12}$ kpc for NGC 281-W, and $1.59^{+0.07}_{-0.06}$ kpc for S 255. The distances and proper motions yield the full space motions of the star-forming regions hosting the masers, and we find that these regions lag circular rotation on average by $sim$17 km s$^{-1}$, a value comparable to those found recently by similar studies.