You are playing under Japanese rules, which means that Black is dead and White wins.
This is because, in playing out captures to determine the life and death status, to recapture a particular ko, you must first make a “pass for that ko”, i.e. point to the ko and dedicate a pass specifically to it. Black can never recapture at A5, since after his pass, White can already capture Black who is in atari.
See here under “Life-and-Death Example 8”.
One point that I myself do not understand about Japanese rules is that there is no superko except No result by mutual agreement. If Black does not want to go to scoring, because he would lose, can’t he play on forever without restrictions on capture? I don’t think the rules deal with this situation.