  The dynamical triangulations approach to quantum gravity is investigated in
detail for the first time in five dimensions. In this case, the most general
action that is linear in components of the f-vector has three terms. It was
suspected that the corresponding space of couplings would yield a rich phase
structure. This work is primarily motivated by the hope that this new viewpoint
will lead to a deeper understanding of dynamical triangulations in general.
Ultimately, this research programme may give a better insight into the
potential application of dynamical triangulations to quantum gravity. This
thesis serves as an exploratory study of this uncharted territory.
  The five dimensional (k,l) moves used in the Monte Carlo algorithm are proven
to be ergodic in the space of combinatorially equivalent simplicial
5-manifolds. A statement is reached regarding the possible existence of an
exponential upper bound on the number of combinatorially equivalent
triangulations of the 5-sphere. Monte Carlo simulations reveal non-trivial
phase structure which is analysed in some detail. Further investigations deal
with the geometric and fractal nature of triangulations. This is followed by a
characterisation of the weak coupling limit in terms of stacked spheres. Simple
graph theory arguments are used to reproduce and generalise a well-known result
in combinatorial topology. Finally, a comprehensive study of singular
structures in dynamical triangulations is presented. It includes a new
understanding of their existence, which appears to be consistent with the
non-existence of singular vertices in three dimensions. The thesis is concluded
with an overview of results, general discussion and suggestions for future
work.
