The years following 2009 marked a shift in the structure of the "Big Four" with Tottenham Hotspur and Manchester City both breaking into the top four. In the 2009–10 season, Tottenham finished fourth and became the first team to break the top four since Everton in 2005. Criticism of the gap between an elite group of "super clubs" and the majority of the Premier League has continued, nevertheless, due to their increasing ability to spend more than the other Premier League clubs. Manchester City won the title in the 2011–12 season, becoming the first club outside the "Big Four" to win since 1994–95. That season also saw two of the Big Four (Chelsea and Liverpool) finish outside the top four places for the first time since 1994–95.
In the 2009-10 season, which team was the first to break into the "Big Four" since 2005?
Tottenham
In the 2009-10 season, Tottenham finished fourth and became the first team to break into the top four since Everton in 2005.
Thus, given this information from the context it can be inferred that Tottenham is the correct answer to this question..