A teacher collects the test scores of 5 students in a math exam. The scores are as follows: 70, 85, 90, 65, and 80. One student retakes the test and improves their score to 95. Calculate the new median score after the retake. Additionally, determine the total increase in the overall sum of the scores after the retake. Let's think step by step and output the final answer within \boxed{}.
user