The major decision taken at the fifth BRICS summit was the establishment of a new development bank. This decision signifies the cooperation and unity among the BRICS countries (Brazil, Russia, India, China, and South Africa) in economic matters. The establishment of this bank is significant because it aims to provide financial support and assistance to infrastructure and development projects in the BRICS countries and other developing nations.

Option 2, reformation of the United Nations, was not a major decision taken at the summit. Although the BRICS countries have called for reforms in the United Nations to make it more inclusive and representative, this specific decision was not made at the fifth BRICS summit.

Option 3, common military exercise, was also not a major decision taken at the summit. While the BRICS countries have engaged in military exercises and cooperation in the past, it was not a key outcome of the fifth summit.

Option 4, cultural exchange among the BRICS countries, was not a major decision taken at the summit. While cultural exchange and cooperation among the BRICS countries are important, it was not the main focus of the fifth summit.

In conclusion, the correct major decision taken at the fifth BRICS summit was the establishment of a new development bank, which aims to