We have studied the effects of 5d transition elements (X = W, Re, Ir, and Pt) on the magnetocrystalline anisotropy energy (MAE) of epitaxially grown hexagonal-close-packed (hcp)-Co single crystal films. The MAE of Co-X significantly changes, depending on X. With increasing numbers of valence electrons in X, the sign of the first anisotropy constant K₁ changes from positive to negative, indicating that the easy axis of magnetization rotates from the c-axis to the c-plane. The second anisotropy constant K₂ monotonically increases with the number of valence electrons in X. All these variations were found to be systematic and are discussed in conjunction with the structural analyses.