We present a measurement of the proper motion of the presumed pulsar in the evolved composite supernova remnant ( SNR ) MSH 15-5 6 whose pulsar wind nebula ( PWN ) has been disrupted by the supernova ( SN ) reverse shock . Using Chandra X-ray observations acquired over a baseline of 15 years , we measure a pulsar velocity of 720 ^ { +290 } _ { -215 } \ > km\ > s ^ { -1 } and a direction of motion of 14 ^ { \circ } \pm 22 ^ { \circ } west of south . We use this measurement to constrain a hydrodynamical model for the evolution of this system and find that its morphology is well-described by an SNR expanding in an ambient density gradient that increases from east to west . The effect of the density gradient and the pulsar ’ s motion is an asymmetric interaction between the SN reverse shock and the PWN that displaces the bulk of the PWN material away from the pulsar , towards the northeast . The simulation is consistent with an SNR age of 11,000 years , an SN ejecta mass of 10 M _ { \odot } , and an average surrounding density of 0.4 \ > cm ^ { -3 } . However , a combination of a higher SN ejecta mass and ambient density can produce a similar SNR morphology at a later age .