If avada kedavra is unblockable (except when an object comes in between the victim and the castor), why didn't Voldemort use it against Dumbledore during their battle at the Ministry in book 5? Was he just so arragant that he thought he could defeat Dumbledore with other magic, to prove he was superior?
He did as described on wiki
Voldemort again Disapparated and Apparated in the middle of the fountain, sending another Killing Curse at Dumbledore. The snake and the curse nearly struck simultaneously, but Fawkes the phoenix sacrificed himself by diving into the path of the curse. He burst into flames and was immediately reborn as a tiny, featherless phoenix.
I was able to find exact part of book in chapter "The Only One He Ever Feared"
Voldemort raised his wand and another jet of green light streaked at Dumbledore, who turned and was gone in a whirling of his cloak. Next second, he had reappeared behind Voldemort and waved his wand towards the remnants of the fountain. The other statues sprang to life.
"It was foolish to come here tonight, Tom,' said Dumbledore calmly. The Aurors are on their way".
"By which time I shall be gone, and you will be dead!" spat Voldemort. He sent another killing
curse at Dumbledore butmissed, instead hitting the security guard's desk, which burst into flame.
Another jet of green light flew from behind the silver shield. This time it was the one-armed centaur, galloping in front of Dumbledore, that took the blast and shattered into a hundred pieces.
`Look out!' Harry yelled.
But even as he shouted, another jet of green light flew at Dumbledore from Voldemort's wand
and the snake struck
Fawkes swooped down in front of Dumbledore, opened his beak wide and swallowed the jet
of green light whole: he burst into flame and fell to the floor, small, wrinkled and flightless.