Elephant Shrews belong to the super-order Afrotheria which includes Aardvarks, dugongs, manitees, hyrax and elephants.
Based on DNA analysis, they split apart from elephants around 105 million years ago, so the relationships are not all that close.
blueplum post #15: "...and if the elephant (or mouse) DNA branched into so many variations, why didn’t gorilla DNA? (I know the Christian answer but I’m always interested in the evolutionist perspective)"
HiTech RedNeck post #17: "Evo answer would be: LUCK"
No, the explanation is that separation of elephants from elephant-shrews took place around 105 million years ago, making them only distantly related.
By contrast: separations of pre-humans from gorillas (7), chimps (5) & orangutans (12) all happened within the past few million years.
That's why we are more closely related to great apes than elephants are to elephant-shrews.