Looks like Skye is booked up in May, is this possible?
Yes, I’m booked for Skye in May and booked last November. At that time, accommodation was hard to get.
I was told by my lodging that May is the most popular month on Skye.
May is a very busy and popular time in Skye. Have a look on booking.com and airbnb as many smaller providers use those platforms rather than having their own websites (it's cheaper for them). Also there is a Facebook group called Skye Rooms that aims to find late availability rooms for travellers. Another shout could be either The Dunvegan or Atholl House Hotels, both small hotels in Dunvegan which sometimes have late availability. Both do food too.