5. On New Year's Day, January 1st, the Elderly Sage was reflecting on his life. He noticed that over the past 5 years, all days of the week had been equally represented, and 10 years ago, the New Year's celebration fell on a Friday. On which day of the week did the sage's somber reflections take place? It is known that the sage's reflections occurred in the $21-\mathrm{m}$ century. Don't forget to explain your answer.
5. Offset. For Thursday. Solution In a common year, there are 365 days, which is 52 weeks and one extra day. In a leap year, there are 52 weeks and two extra days. From the condition, it follows that over the last five years of the Sage's life, due to the additional days, exactly one week has accumulated. Therefore, during this five-year period, there were two leap years: the first and the last. This means that during the previous five-year period, there was only one leap year (the second), and over the ten years, there were three leap years. This means that over the entire 10 years, in addition to the whole number of weeks, 10 + 3 = 13 days have accumulated, which is two weeks minus one day. But 10 years ago, the New Year's holiday fell on a Friday, and this year it fell on a Thursday.

Criteria: correct reasoning and correct answer - 7 points; correctly described the two previous five-year periods, but incorrect answer - 5 points; concluded that over the last five years of the Sage's life there were two leap years, but no further progress or incorrect progress - 1 point; correct answer with verification (by the placement of leap years) - 2 points; only answer - 0 points.