R5Pd2 compounds are known to exhibit magnetic glass transition and large cooling power in the cryogenic temperature region. All the R5Pd2 (R = Ho, Dy, Dy0.6Gd0.4) compounds crystallize in the cubic Dy5Pd2-type of structure (space group Fd3m). The compounds Ho5Pd2, Dy5Pd2, and (Dy0.6Gd0.4)(5)Pd-2 undergo a paramagnetic to glass transition at 27 K, 38 K, and 58.5 K with a small hump at 10 K, 14 K, and 20 K respectively, confirming the double glass transitions present in these compounds. The maximum isothermal magnetic entropy changes (- Delta S-max) for the compounds Ho5Pd2, Dy5Pd2, and (Dy0.6Gd0.4)(5)Pd-2 are 19.95 J/kg-K, 7.89 J/kg-K, and 7.4 J/kg-K with RCP values 987 J/kg, 549 J/kg, and 673 J/kg respectively for magnetic field change of 70 kOe. However, there is a controversy regarding the order of magnetic phase transition present in these compounds. A detailed investigation on the order of magnetic phase transition in Ho5Pd2, Dy5Pd2, and (Dy0.6Gd0.4)(5)Pd-2 compounds has been studied. Heat capacity measurements give a fingerprint of the absence of first-order magnetic phase transitions in these compounds. Field dependent magnetic entropy change studies on these compounds confirm the second-order nature of magnetic phase transitions.