  We study the compactification of M-theory on Calabi-Yau five-folds and the
resulting N=2 super-mechanics theories. By explicit reduction from 11
dimensions, including both bosonic and fermionic terms, we calculate the
one-dimensional effective action and show that it can be derived from an N=2
super-space action. We find that the Kahler and complex structure moduli of the
five-fold reside in 2a and 2b super-multiplets, respectively. Constrained 2a
super-multiplets arise from zero-modes of the M-theory three-form and lead to
cross-couplings between 2a and 2b multiplets. Fermionic zero modes which arise
from the (1,3) sector of the 11-dimensional gravitino do not have bosonic
super-partners and have to be described by purely fermionic super-multiplets in
one dimension. We also study the inclusion of flux and discuss the consistency
of the scalar potential with one-dimensional N=2 supersymmetry and how it can
be described in terms of a superpotential. This superpotential can also be
obtained from a Gukov-type formula which we present. Supersymmetric vacua,
obtained by solving the F-term equations, always have vanishing vacuum energy
due to the form of this scalar potential. We show that such supersymmetric
solutions exist for particular examples. Two substantial appendices develop the
topology and geometry of Calabi-Yau five-folds and the structure of
one-dimensional N=2 supersymmetry and supergravity to the level of generality
required for our purposes.
