The first day of a new lustrum is a holiday because 1 lustrum = 5 years, so it is also the first day of the year. And most of our lives is organized in yearly cycles, so I think it makes sense to mark the beginning of a new one with a holiday (even more so where I live, since our school year matches the actual year and most people take a summer vacation in January or February). It's also a good chance to make plans for the year that's just begun.
And I think it's also the only holiday that applies to everyone on TPM.