The present invention relates to monospecific or bispecific antibody molecules that specifically bind the human DR5 antigen. The invention relates in particular to DR5-specific antibody molecules of the IgG1 isotype having a mutation in the Fc region that enhances clustering of IgG molecules after cell-surface antigen binding leading to the induction of DR5 signaling, apoptosis and cell death. The invention further relates to a combination of antibody molecules binding different epitopes on DR5. The invention also relates to pharmaceutical compositions containing these molecules and the treatment of cancer using these compositions.