RCo5-type (R=light rare earth) medium- and high-entropy intermetallic compounds, which are designed by random occupation of equiatomic multiple rare earth elements at the rare earth site, are prepared by arc melting and vacuum heat-treatment technologies, and their crystal structures and magnetic properties are studied by X-ray diffraction and magnetic measurements. The empirical electron theory of solids and molecules is used to investigate their valence electron structures, thermal and magnetic properties. The theoretical bond lengths and magnetic moments match the experimental ones well. The study reveals that the thermal and magnetic properties are strongly related to the valence electron structures modulated by medium- and high-entropy design at rare earth. The medium and high entropized designs induce the increase of the covalence electron numbers nc. It is helpful for stabilizing the crystal structure. The number of covalence electron pair of the strongest R-CoI bond affects the melting point. The magnetic moments of RCo5-type medium- and high-entropy intermetallic compounds, which mainly originate from the 3d magnetic electrons of Co atoms, are modulated by medium and high entropized rare earth due to their exchange interactions. The magnetic moment of Co at the 2c site is larger than that of Co at the 3g site, which is due to the electron transformations from magnetic to covalence electron for bonding with the rare earth at the 3g site. Curie temperatures raise with the increasing 3d magnetic electron numbers of Co atom.