5, 10, and 13, I think.
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The Dallas Cowboys have lost three Super Bowls:
Super Bowl V, Baltimore Colts won 16-13.
Super Bowl X, Pittsburgh Steelers won 21-17.
Super Bowl XIII, Pittsburgh Steelers won 35-31.
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The Dallas Cowboys lost to the Baltimore Colts in the Super Bowl before the team relocated and became the Indianapolis Colts and they then lost to the Pittsburgh Steelers twice afterwards though not consecutively.
Five. The Cowboys lost back-to-back NFL title games to the Green Bay Packers during the 1966 and 1967 seasons. They also lost three Super Bowls contests (Super Bowl V, Super Bowl X and Super Bowl XIII).