ABSTRACT: Chung has defined a pebbling move on a graph G to be the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number, f(G), of a graph is the least number of pebbles such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified, but arbitrary, vertex. Graham’s Conjecture states: for any graphs G and H, f(G * H) ≤ f(G)f(H). Herscovici and Higgins showed that Graham’s conjecture holds when G=H=C₅. I will give details of a shorter – and hopefully generalizable – proof of this result.