we discuss a new method to bound 5-torsion in class groups using elliptic curves. the most natural ``trivial'' bound on the n-torsion is to bound it by the size of the entire class group, for which one has a global class number formula. we explain how to make sense of the n-torsion of a class group intrinsically as a ``dimension 0 selmer group'', and by embedding it into an appropriate elliptic curve we can bound its size by the tate-shafarevich group which we can bound using the bsd conjecture. this fits into a general paradigm where one bounds ``dimension 0 selmer groups'' by embedding into global objects, and using class number formulas.