Welcome, Newclimber,

May is pretty early to hike Mt Whitney. There is sure to be a snowpack, and the switchbacks will be inaccessible due to the amount of snow. At that time of year, few people go, but there will be tracks in the snow, with people heading all over the place -- many in wrong directions in the lower parts of the trail.

Once you get to the 12,500 ft elevation and Trail Camp, people head up the slope west of the switchbacks using crampons, and an ice axe just in case of a slip. Be sure to view John Li's report and video here: 6/1/2014 Dayhike Summit by beginner hikers

As for permits, there are always walk-in permits available early in May, so you won't have any trouble with that. Due to the tougher conditions, making it as a day hike is possible only for the most fit (and lucky if altitude issues don't strike). Camping overnight at Outpost Camp (10,400 ft, 3200 M) would make the hike easier. (Camping there two nights would get you much better acclimated for the peak, too. As for acclimation, I would get a prescription for Diamox (acetazolamide) and take it a trial dose at home to make sure it doesn't have any adverse side effects.)

If you are serious about this climb, then learn everything you can about the altitude and hiking in snow. If you take your time, and practice with the ice axe once you get to a slope where you can try, you might be ok. Most importantly, turn around if you get out of your comfort level, or if the weather is bad. People die on Whitney every year. The mountain will always be there for another try later.

Here are some links on ice axe use:
Watching this video by the British Mountaineering Council is mandatory:   Mt Whitney hiking and climbing videos
Another good one:  Ice Axe Technique
Related: Glissading from Trail Crest and hazards