  In this work we present 3-algebraic constructions and representations for
three-dimensional N = 5 supersymmetric Chern-Simons theories, and show how they
relate to theories with additional supersymmetries. The N = 5 structure
constants give theories with Sp(2N) \times SO(M) gauge symmetry, as well as
more exotic symmetries known from gauged supergravity. We find explicit lifts
from N = 6 to 8, and N = 5 to 6 and 8, for appropriate gauge groups.
