I am afraid "Google" is wrong about May in Alaska. Since Google simply links you to various websites based on your search terms, which website did you see that said this?
It is a huge state with many climate zones. There might be somewhere in the southern regions where you could hike in May, but for most of the state that is still early spring, with melting snow, mud, no green leaves, and no wildflowers. It might not rain as much, but that is small comfort when the ground is still soggy, muddy, and/or snowy.
The weather does tend to be good in June, when summer starts all at once. It is probably the month with lowest rainfall, but the most mosquitoes. I had lovely weather and wildflowers the last time I was there, mid-June.
I lived there for seven years when I was younger, and have returned to visit and hike three times in the last five summers. I love it there. And I would not go to the mainland, especially Interior or Southcentral, in May. If I thought I would enjoy a cruise, I might consider a May cruise up the Inside Passage (Southeast Alaska) to Juneau and/or Glacier Bay because the scenery is still spectacular. But I would not plan on hiking.
Bear viewing is best where there are salmon runs. That means July at famous bear-viewing places places like Brooks Falls, Anan Bear Reserve, etc. There is a good salmon run up the Copper River in May, but I know of no bear-watching spots anywhere near there. That river is too high and fast for the bears to fish.
Bears can be seen anytime in the summer in Denali National Park, but they are not fishing.
Dogsledding in summer is either on bare ground on a wheeled "sled", or on real snow at higher elevations, usually accessed by helicopter. I was not aware of any on snow near Skagway in August, but maybe Jill will be driven up high enough somewhere? Mushing on a real sled on snow is lots of fun, but I would not bother with the "summer sled" experience on bare ground.
Like Sasha, I live near Vancouver, and would regard either that city or nearby Victoria as a good destination in May. From Vancouver you could drive up to Whistler for some hiking, not on the high slopes where there may still be snow, but lower down it should be OK. We do not hike in the higher elevations of the Cascades ( above 5,000 feet) until July most years. And one summer were still BA kcountry skiing on good snow in July. But at sea level May is snow-free and really nice. (Although 2017 we had record rainfall that month).