The cinquefoils are easily recognized and found all around the world. There are about 400 species of cinquefoil, genus
Potentilla (rose family, Rosaceae). They have five petals, like a basic rose flower, but never have thorns. The most common one in Europe had five-lobed leaves as well as five-petaled flowers, so was called cinque-foil, meaning 5-(lobed)-leaf. American species--about 98 native species!, tend to have more lobes than five, so the name carried over but doesn't fit very well.
In North America, almost all the cinquefoils/ Potentilla species are herbs, nonwoody plants.
So I easily learned shrubby cinquefoil, Potentilla fruticosa, because it shares the flower and leaf shape, but is a shrub, the only shrubby cinquefoil in Colorado (and the U.S.) Since it was (is) so distinctive, I shouldn't have been surprised that taxonomists, revising the very big genus Potentilla, gave the shrubby cinquefoils a genus of their own; Potentilla fruticosa became Dasiphora fruticosa. The shrubby cinquefoil group, Dasiphora, is a genus of about 12 species. Only one is found wild in North America, the others are Eurasian. Since Potentilla is a very confusing group, separating out the shrubby cinquefoils made Potentilla a little more uniform (no shrubs!).