This problem involves some algebra and the concept of linear equations. Let me start by assigning some variables to represent the ages of the father and the son. I will use F to denote the father's age today, and S to denote the son's age today. The first sentence tells me that F = 5S, which is a linear equation relating the two variables. The second sentence tells me that F - 3 + S - 3 = 30, which is another linear equation involving F and S. I can use the first equation to substitute for F in the second equation, since I know that F = 5S. This gives me 5S - 3 + S - 3 = 30, which simplifies to 6S - 6 = 30. Adding 6 to both sides, I get 6S = 36, and dividing by 6, I get S = 6. This means that the son's age today is 6 years old. To check my answer, I can plug it back into the first equation and see if it satisfies the second equation. If S = 6, then F = 5S = 5 * 6 = 30. Then F - 3 + S - 3 = 30 - 3 + 6 - 3 = 30, which is correct. Therefore, I am confident that my answer is correct. 
Today a father's age is five times his son's age. Exactly three years ago, the sum of their ages was 30. How old is the son today?