Aims. We study the connection between spatially resolved star formation and young star clusters across the disc of M51. Methods. We combine star cluster data based on B, V, and I-band Hubble Space Telescope ACS imaging, together with new WFPC2 U-band photometry to derive ages, masses, and extinctions of 1580 resolved star clusters using SSP models. This data is combined with data on the spatially resolved star formation rates and gas surface densities, as well as Halpha and 20cm radio-continuum (RC) emission, which allows us to study the spatial correlations between star formation and star clusters. Two-point autocorrelation functions are used to study the clustering of star clusters as a function of spatial scale and age. Results. We find that the clustering of star clusters among themselves decreases both with spatial scale and age, consistent with hierarchical star formation. The slope of the autocorrelation functions are consistent with projected fractal dimensions in the range of 1.2-1.6, which is similar to other galaxies, therefore suggesting that the fractal dimension of hierarchical star formation is universal. Both star and cluster formation peak at a galactocentric radius of 2.5 and 5 kpc, which we tentatively attribute to the presence of the 4:1 resonance and the co-rotation radius. The positions of the youngest (<10 Myr) star clusters show the strongest correlation with the spiral arms, Halpha, and the RC emission, and these correlations decrease with age. The azimuthal distribution of clusters in terms of kinematic age away from the spiral arms indicates that the majority of the clusters formed 5-20 Myr before their parental gas cloud reached the centre of the spiral arm.