I guess I got it wrong on the Islanders not winning five in a row going back to December of 1993. They did win five in a row during the 2002-03 season which a few media outlets did point out today and it turns out they are correct:
Dec. 23 Montreal Canadiens W 3-1
Dec. 28 Carolina Hurricanes W 3-0
Dec. 30 Florida Panthers W 2-1 OT
Dec. 31 at Buffalo Sabres W 1-0 OT
Jan. 3 Boston Bruins W 8-4
Islanders also had a six game winning streak during the 2003-04 season.