Why does it say "2+2=5" in the book 1984?
Orwell borrowed this from Assignment in Utopia by Eugene Lyons concerning his time in the Soviet Union when Stalin was in power. Stalin used the slogan "2+2=5" as a symbol for his idea that the Soviet Union would complete a five-year plan in four years. This is a tongue-in-cheek example of the power of propaganda. In countries with an oppressive regime, such as Stalin's Soviet empire, propaganda becomes necessary to promote the regime's ideology while suppressing subversives. When such regimes become very powerful, they can use propaganda to create truth, or the appearance of truth.
The reason Winston uses this phrase is because he recognizes the great power of Big Brother. He realizes that the party is so powerful that if they promote an absurd idea such as "2+2=5" people will believe it simply because the party has such ubiquitous control over everything. Winston holds onto the hope that the human mind is still somewhat free. For Winston, freedom is to believe actual truth, i.e., 2+2=4.