Isn’t ’mezonot’ reserved for the five cereals associated with Eretz Yisrael - wheat, barley, oats, spelt and rye? Shouldn’t we make ’ha’adama’ on rice?

The poskim saw rice as something a bit different, although it is not of the five species of grain. Since it is nourishing and filling it attains the status of a grain and therefore when cooked a "mezonot is said . But after eating rice only "boreh nefashot" is said because "Al Hamichya was established only for the Shivat Haminim" (See Shulchan Aruch 208:7 , Mishna Brura 208:28)