In reply to MuzzaSA:
I couldn't comment on average conditions in late May as I've only been up there in Aug and Sept, other than to say it could vary enormously. However I would say that the face with the fixed ropes is in shade until midday ish and can be very cold indeed before that, even in August, so probably even more so in May.
If you're wanting to do a bare hands and rock shoe ascent I'd pick a day when there's next to no chance of an afternoon storm and head up lateish with the aim of not getting on the face before the sun.
You could do this from the the first cable car (check operating times in May) but would probably miss the last one down.
Going in May should make the approach and descent slopes rather more pleasant than they are in August, snow instead of rubble.