Cayman Islands is about 5,611 times smaller than Alaska.

Alaska is approximately 1,481,348 sq km, while Cayman Islands is approximately 264 sq km, making Cayman Islands 0.02% the size of Alaska. Meanwhile, the population of Alaska is ~710,231 people (645,922 fewer people live in Cayman Islands).
Tip: This to-scale comparison of Alaska vs. Cayman Islands uses the Mercator projection, which distorts the size of regions near the poles.