Which has ballistics similar to the 5.56 NATO round, depending on which version of each basic type one is speaking of. The round probably wouldn't even exit, depending on shot placement of course. It could tear up a lot of meat though. Both the 5.45 and 5.56 (.223) are designed to yaw after striking flesh. (they become hydrodynamically unstable). They also often break up. The 5.56 is slightly heavier and slightly faster, but not enough to really matter much, at least until you go to the newer 62gr 5.56, which then are slighly slower than the 53gr 5.45 rounds. (All in their military loadings) See Wound Ballistics
Bottom line, your 5.45x39 is no more appropriate for larger sized deer than the 5.56, although both will do the job if you can do yours.