  Despite being one of the best-known galaxies, the distance to the Whirlpool
Galaxy, M 51, is still debated. Current estimates range from 6.02 to 9.09 Mpc,
and different methods yield discrepant results. No Cepheid distance has been
published for M 51 to date. We aim to estimate a more reliable distance to M 51
through two independent methods: Cepheid variables and their period-luminosity
relation, and an augmented version of the expanding photosphere method (EPM) on
the Type IIP SN 2005cs. For the Cepheid variables, we analyse a recently
published HST catalogue of stars in M 51. By applying light curve and
colour-magnitude diagram-based filtering, we select a high-quality sample of M
51 Cepheids to estimate the distance through the period-luminosity relation.
For SN 2005cs, an emulator-based spectral fitting technique is applied, which
allows for the fast and reliable estimation of physical parameters of the
supernova atmosphere. We augment the established framework of EPM with these
spectral models to obtain a precise distance to M 51. The two resulting
distance estimates are D_Cep = 7.59 +/- 0.30 Mpc and D_2005cs = 7.34 +/- 0.39
Mpc using the Cepheid period-luminosity relation and the spectral modelling of
SN 2005cs respectively. This is the first published Cepheid distance for this
galaxy. Given that these two estimates are completely independent, one may
combine them, which yields D_M51 = 7.50 +/- 0.24 Mpc (3.2% uncertainty). Our
distance estimates are in agreement with most of the results obtained
previously for M 51, while being more precise than the earlier counterparts.
They are however significantly lower than the TRGB estimates, which are often
adopted for the distance to this galaxy. The results highlight the importance
of direct cross-checks between independent distance estimates for quantifying
systematic uncertainties.
