Where did you find those figures? I heard that the DNA of chimpanzees is 98% identical to ours. (BTW, does this mean that halibuts can climb trees? Or that a chimp eating a banana is almost committing cannibalism? )
More seriously, you shouldn't be surprised if we share a large part of our DNA with plants and bacteria. Most genes seem to encode for the basic chemistry of the cell. Add to that the fact that 95% is junk DNA that doesn't seem to encode for anything, and the differences become very small indeed. (Alternatively, you might also say that these similarity figures are bloody useless. :razz
I can't remember the exact place i got the info from, but these "facts" have been doing the rounds in the creationists v's evolutionists debate for years