A search for hidden-charm pentaquark states decaying to a range of ςcD¯ and Λc+D¯ final states, as well as doubly charmed pentaquark states to ςcD and Λc+D, is made using samples of proton-proton collision data corresponding to an integrated luminosity of 5.7 fb-1 recorded by the LHCb detector at s=13 TeV. Since no significant signals are found, upper limits are set on the pentaquark yields relative to that of the Λc+ baryon in the Λc+→pK-π+ decay mode. The known pentaquark states are also investigated, and their signal yields are found to be consistent with zero in all cases.