It is the current local time right now in George Town, West Bay, Bodden Town, East End, North Side and in all Cayman Islands’ cities. 
Cayman Islands’ time zone: EST or UTC-05:00

No daylight saving time (DST) in Cayman Islands.

Full name: Cayman Islands
Continent: North America
Region: Caribbean
Population: 44,270
Area: 262 km²
Capital: George Town
Currency: Dollar (KYD)
Phone code: +1-345
Domain: .ky
Wikipedia article: Cayman Islands