The ratio of wine to water in bottle A is 5: 3, and the ratio of wine to water in bottle B is 5: 4. Now take the two bottles of solution at 5: 6 and mix them. What is the ratio of wine to water in the new mixture?
Please show your work with detailed steps and express your answer in simplified ratio A:B where A and B are positive integers. DO NOT use scientific notation and DO NOT round up/down your answer.