If it's strictly starting in 2005, then it's Tsubasa Chronicle, followed by Mai Otome. Both have great stories and the great music by one of the best female composers to grace the anime scene.
If it's just anime shown in 2005 then it has to be Bleach for me.
Here's my list in no particular order:
Bleach
Tsubasa Chronicle
Mai HiME
Mai Otome
Yakitate Japan!
Monster
and Naruto (before it went into fillers
)
Special mention must be given to Gundam SEED Destiny as the most bashed show of the year, if not the worst excuse of an anime.