The distance to the Whirlpool galaxy, M 51, is still debated, even though the galaxy has been studied in great detail. Current estimates range from 6.02 to 9.09Mpc, 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 supernova SN 2005cs, which exploded in this galaxy. For the Cepheid variables, we analysed a recently published Hubble Space Telescope catalogue of stars in M 51. By applying filtering based on the light curve and colour-magnitude diagram, we selected 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 was applied, which allows for the fast and reliable estimation of the physical parameters of the supernova atmosphere. We augmented 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+/-0.30Mpc and D_2005cs_=7.34+/-0.39Mpc using the Cepheid period-luminosity relation and the spectral modelling of SN 2005cs, respectively. This is the first published Cepheid distance for this galaxy. The obtained values are precise to 4-5% and are fully consistent within 1{sigma} uncertainties. Because these two estimates are completely independent, they can be combined for an even more precise estimate, which yields D_M51_=7.50+/-0.24Mpc (3.2% uncertainty). Our distance estimates agree with most of the results obtained previously for M 51, but they are more precise than the earlier counterparts. However, they are 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 so that systematic uncertainties can be quantified. Because of the large discrepancy, this finding can also affect distance-sensitive studies and their discussion for objects within M 51, as well as the estimation of the Hubble constant through the type IIP standardizable candle method, for which SN 2005cs is a calibrator object.