Diversity Visa Fairness Act of 2005 - Amends the Immigration and and Nationality Act with respect to the diversity visa lottery program to permit an alien to remain eligible for a diversity visa or status adjustment beyond the fiscal year of acceptance if: (1) the visa or status adjustment was properly applied for during the fiscal year of selection; and (2) notice of application authorization was given through publication in the Visa Bulletin.

Authorizes reopening of a prior fiscal year visa lottery application if: (1) the alien was eligible for, and properly applied for, status adjustment during FY1998-FY2004; (2) the application was denied because the Department of Homeland Security (DHS) or the Immigration and Naturalization Service (INS) failed to adjudicate the application during the fiscal year of application; (3) the alien moves to reopen the application; and (4) the alien has continuously resided in the United States since submitting the application.