Will you have to clear U.S. Customs and Immigration upon your arrival at JFK? Will you have checked baggage to claim? If so, does your inbound airline have an interline baggage agreement with your outbound airline, so that you can re-check the bags at Terminal 1 after you clear Customs? These factors can affect whether you will make your connection.
Getting from Terminal 1 to Terminal 5 should only take about ten minutes: you can take any AirTrain, in either direction.
Will you have to clear U.S.