  We present a comprehensive study of the X-ray emission from SNR 0453-68.5 in
the Large Magellanic Cloud (LMC) as seen from the \textit{Chandra} X-ray
Observatory. This object is in a class of composite remnants that exhibit a
shell of emission surrounding a central plerion, more commonly known as a
pulsar wind nebula (PWN). This is one of only five remnants in the LMC with an
identified PWN. We find that the shell of emission is not ejecta dominated, but
rather due to shocked ISM that has been swept up by the supernova blast wave or
located in a precursor cavity wall. This is supported by the morphology of the
local molecular cloud as seen with the \textit{Spitzer} Space Telescope. The
spectral properties are consistent with a middle-aged remnant $>$17000 years
old. A point source detected within the central knot is determined to be the
pulsar powering the synchrotron emission of the PWN. Spectral fits show the
nebula is well characterized by a power law with photon index $\Gamma=2.0$.
This index is constant over a spatial scale of 0.4-1.2 pc, which is
inconsistent with younger PWN containing remnants such as the Crab Nebula and
SNR 0540-69.3. These fits also contain significant contributions from an ejecta
dominated thermal plasma which we interpret as evidence of mixing during an
evolved interaction of the PWN with the reverse shock of the SNR. We observe no
evidence that the central pulsar contains a significant velocity transverse to
the line of sight and argue that despite the asymmetric surface brightness
distribution the SN explosion giving birth to this remnant may have been quite
symmetric.
