The production of D^0, D^*+, D^+, D_s+ and Lambda_c^+ charm hadrons and their antiparticles in ep scattering at HERA has been studied with the ZEUS detector, using a total integrated luminosity of 372 pb^-1. The fractions of charm quarks hadronising into a particular charm hadron were derived. In addition, the ratio of neutral to charged D-meson production rates, the fraction of charged D mesons produced in a vector state, and the stangeness-suppression factor have been determined. The measurements have been performed in the photoproduction regime. The charm hadrons were reconstructed in the range of transverse momentum p_T >3.8 GeV and pseudorapidity |eta|<1.6. The charm fragmentation fractions are compared to previous results from HERA and from e+e-experiments. The data support the hypothesis that fragmentation is independent of the production process