  We present a construction in Matrix theory of longitudinal 5-branes whose
geometry in transverse space corresponds to a 4-sphere. We describe these
branes through an explicit construction in terms of N*N matrices for a
particular infinite series of values of N. The matrices used in the
construction have a number of properties which can be interpreted in terms of
the 4-sphere geometry, in analogy with similar properties of the SU(2)
generators used in the construction of a spherical membrane. The physical
properties of these systems correspond with those expected from M-theory; in
particular, these objects have an energy and a leading long-distance
interaction with gravitons which agrees with 11D supergravity at leading order
in N.
