What are the five most significant events in 1776 by David McCollough, not focusing only on the military engagements?

It is, of course, difficult to point to exclusively non-military events in a book that focuses so much on the Revolutionary War. So there are some events in this answer that are basically military. Still, some are more political in nature. 

The first event actually occurs in October of 1775. After a speech by King George and a lengthy debate in Parliament, with significant dissenting voices, both houses of Parliament voted to approve Lord North's plan to send a large military and naval force to the colonies, then in a state of all-out rebellion. This marked, in many ways, a point of no return in the conflict and was thus a major event. Another occurred in March of 1776, when Washington's capture and fortification of Dorchester Heights forced the British army to abandon the city of Boston. McCullough describes this event as the "first thrilling news of the war" for the rebels (108). 

Another event, of course, was the decision of the Second Continental Congress to declare independence from Great Britain. This decision, reached on July 2, meant that the war would be an "all-out war for an independent America" and was a major turning point described in the book (137). But this occurred even as another crucial event was taking place--the massive invasion of New York by the British army and navy. Finally, the book closes with a speech by King George in 1777. Echoing the debates in Parliament at the beginning of the book, the speech announced that, despite the previous year's events, the Americans had not "recovered from their delusion" (292).