Let the score of the fifth exam be x, then there are:

The total score of the first five times is 75 * 4+x = 300+x, and the average score of the five times is (300+x)/5;

Because the score of the fifth time is 8 points higher than the average score of the fifth time, so:

x - 8 = (300+x)/5

The solution is x=85.