The disclosure provides a method of reducing the likelihood of forming a T cell-mediated allograft vasculopathy lesion in a mammalian transplant recipient comprising transplanting an allograft from a donor to a recipient and administering a therapeutically effective amount of an anti-C5 antibody, or antigen-binding fragment thereof, to the recipient, wherein the anti-C5 antibody, or antigen-binding fragment thereof reduces the likelihood of forming an allograft vasculopathy lesion in the allograft, compared to the absence of treatment with an anti-C5 antibody, or antigen-binding fragment thereof.