Context. HD 61005 is a nearby young solar type star that shows a large infrared excess due to a debris disk. The disk has been recently imaged from ground and space, with indications of several components. Some characteristics of the disk suggest the presence of planetary companions around the star, that remain undetected in deep adaptive optics imaging. Aims. For a better understanding of the system we aim to refine the determination of the stellar parameters, with emphasis on the stellar age and system orientation. Methods. We used ASAS and Hipparcos photometry and FEROS spectra to determine the rotation period, radial and rotational velocity, chromospheric emission, effective temperature, and chemical composition. Results. We find no indication of any misalignment between the star rotation axis and the disk. The standard age calibrations applied to several indicators yield an age close to that of the Pleiades (120 Myr); however the kinematic properties strongly support its membership in the younger (40 Myr) Argus association, which also includes the IC 2391 open cluster. Detailed comparison of the properties of HD 61005 and IC 2391 members shows that the characteristics of HD 61005 are compatible with membership to the Argus association, once its rather slow rotation is taken into account, because lithium and other age indicators are somewhat correlated with stellar rotation at a fixed age. We also identify systematic differences between the field and cluster population of the Argus association, which are probably selection effects, so we suggest that additional members with slower rotation and lower activity level are waiting to be identified.