Thought of some lame riddle after reading Derek's and Priscilla's blogs. Care to guess?

Who can claim to be I?
Unique and special I, my first is but a poor cousin thrice removed.
Different my second is, estranged from its brothers,
It is missing from this most unusual line.
Zebras favor not my third; neither do
Horses, yet mares do, and I wonder why.
Ordinary four,
Not flower, not grass, but a mirror image of a tree.
Go east, west or south you may, but never
Possibly can you find my fifth.
Arrange the letters in descending
Order, and perhaps you may figure out my whole.

Lol, there are two things present in the riddle. Try guessing. I think you probably can get one but not the other.