The 5th New York Infantry Regiment, formed in May of 1861, was a completely different unit.

In April of 1862 legislation changed the designation of militia units to “National Guard.”

1861
April 19 Tendered service to State
April 27 Eight companies sailed from New York for Fortress Monroe, Va. under the command of Colonel C. Schwarzwaelder, Lieutenant Colonel Louis Burger and Major George Van Amsberg
April 30 Sailed to Annapolis, Md. aboard the steamship Kedar and moved to Washington
May 1 Mustered into United States service for three months at Washington and assigned to the Department of Washington.
May 1-12 Guard duty along railroad from Annapolis to Annapolis Junction
May 12 Moved to Washington, D.C. and quartered in the United States Capital
May 24 Advance into Virginia and occupation of Arlington Heights
May 25 Guard and picket duty
May 28 A company was transferred in from the 2nd New York State Militia, becoming Company K
June 3 Camp on Meridian Hill
July 7 Moved by rail to Baltimore, then to Hagerstown, Md.
July 9-10 To Martinsburg, Va. Attached to Butterfield’s Brigade, Sandford’s Division, Patterson’s Army.
July 15 Advance to Bunker Hill
July 17 To Smithfield, then to Charlestown.
July 21 Moved to Harper’s Ferry and duty at Bolivar Heights
July 28 Moved to Knoxville, Md.
August 2 To New York City
August 7 Mustered out

1863

June Entered in the service of the United States for thirty days under Colonel Louis Burger
June 18 Left State for Harrisburg, Pa.
June 19 –
July 17
Guard duty at Harrisburg, Marysville, Carlisle and Chambersburg, Pa. attached to Yates’ 1st Brigade, Dana’s Division, Dept. of the Susquehanna.
July 22 Mustered out of United States service in New York