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The prime factors of 365 is 5 and 73, hence a month should either be 73 days and there should be 5 of them, or there should be 73 months with 5 days each.
Mathematical perfection!
Problem here is there's actually 365.25 days in a year, the .25 is why we have leap years.
Ok, thats fine, we'll just... The factors of 365.25 are: 487¹×3¹×2⁻²
Wait....
The problem here is that 0.25 is actually an overestimate by about 3 in every 400 years. That's why we don't have leap years on every hundredth year, but we do have them again every 400. (And, of course, you can get even more precise than that.)
Yeah yeah Georgian reform. Problem it it breaks in 6500
Your mom has leap years
Yes also 364 days from 13x28 would not align with years around the sun. We'd still need a leap year with 5x73 but that's easier than correcting from 364.
12x30, 5 or 6-day intercalary (government-mandated) days off for rest and celebration of Yule + New Year's (just make them all December 31-35/6).