Abstract: Motivated by a prediction of Hayashi, Jefferson, Kim, Ohmori, and Vafa based on a proposed generalization of the topological vertex formalism, the Gromov-Witten or Gopakumar-Vafa invariants of low degree are computed for the mirror quintic, involving all 101 Kahler parameters.  A conjectural description of the Mori cone of the mirror quintic is also proposed, with evidence; however the validity of the computed invariants are not dependent on this conjecture.