  We characterised five transiting planetary systems (HAT-P-3, HAT-P-12,
HAT-P-22, WASP-39 and WASP-60) and determined their sky-projected planet
orbital obliquity through the measurement of the RM effect. We used HARPS-N
high-precision radial velocity measurements, gathered during transit events, to
measure the RM effect in the target systems and determine the sky-projected
angle between the planetary orbital plane and the stellar equator. The
characterisation of stellar atmospheric parameters was performed exploiting the
HARPS-N spectra, using line equivalent width ratios, and spectral synthesis
methods. Photometric parameters of the five transiting exoplanets were
re-analysed through 17 new light curves, obtained with an array of medium-class
telescopes, and other light curves from the literature. Survey-time-series
photometric data were analysed for determining the rotation periods of the five
stars and their spin inclination. From the analysis of the RM effect we derived
a sky-projected obliquity of 21.2 degree, -54 degree, -2.1 degree, 0 degree and
-129 degree for HAT-P-3b, HAT-P-12b, HAT-P-22b, WASP-39b and WASP-60b,
respectively. The latter value indicates that WASP-60b is moving on a
retrograde orbit. These values represent the first measurements of \lambda for
the five exoplanetary systems under study. The stellar activity of HAT-P-22
indicates a rotation period of 28.7 days, which allowed us to estimate the true
misalignment angle of HAT-P-22b, \psi=24 degree. The revision of the physical
parameters of the five exoplanetary systems returned values that are fully
compatible with those existing in the literature. The exception to this is the
WASP-60 system, for which, based on higher quality spectroscopic and
photometric data, we found a more massive and younger star and a larger and
hotter planet.
