I arrived in Huaraz on 12 June 2011. One of my objectives was to climb the two Huascarán peaks, but when I asked around, I learned that the mountain would not be in shape until July. I had time, so I climbed other peaks instead first.
During my time in Peru, early in the season the biggest problem I encountered was deep powder. Even on relatively flat terrain, that's very exhausting stuff. In the first week of June I climbed Ausangate, using snow shoes for the deep powder on the summit plateau, and still it was very hard. In addition, obviously, on steeper slopes, you never know if it will stay up there. I encountered powder above 6000m on relatively flat and undulating terrain, and on steep slopes facing south and southwest just above 5000m. These faces don't get much sun, which would soften the snow. At night it freezes solid again and that helps consolidating the powder.
I didn't ask specifically why Huascarán was not in shape yet in June, but I presume that the snow needed more time to settle or get blown off the mountain. From Garganta at 6000m to about 6300m you have to climb a steep west-facing slope, with lots seracs and crevasses. Above 6300m it's not steep at all and I would expect powder up there. At that elevation it's usually cold enough so the sun doesn't soften up the snow.The icefall below Campo Dos on Huascarán, 10 July 2011
This photo illustrates the problems you might have to face. The route goes around this, but if there is no trail, you have to figure that out for yourself - and with a layer of powder on top, smoothing over all the features, you can't see
that this is beneath you.
And that sums up the two problems that you'll likely face when you go in May or early June. The snow makes the going more difficult, and, being the first in the season, you have to find your own way up.
Normally, going from Campo Uno to Campo Dos is not a very long day, so you can afford to lose some time searching for a route.
Higher up that's different. From Garganta at 6000m to around 6300m you have to find a way through a maze of seracs and crevasses on the west face and if that takes too long, you won't have enough time to make it to the summit. Planning for an extra day, only to scout this part of the route from Campo Dos and mark the trail, would not be a bad idea.
For the record, I consider 2 weeks rather short for Huascarán. First you'll need time to acclimatize, by climbing other peaks. When you're well acclimatized, the mountain is in good shape (and has a trail) and the weather is good, 5 days is pretty fast, but doable. But more often than not you'll need more time, because you might not feel too good or the weather keeps you in your tent.
If all this doesn't stop you, then good luck, and let us know how you fared.