Death during the Gathas

When death occurs, as per tradition, we disregard the Gatha days and count the first Gatha as Hormazd roz and the last Gatha as Spandarmad roz. I would like to differ with this system, pointing out some discrepancies in this traditional method.

Though we take the first Gatha to be Hormazd roz, this roz actually comes five days later. How can we predate the roz?

My layman’s logic tells me that we have a calendar of 360 days, plus five days of Gathas which makes it 365 days (intercalation forgotten!). So the last month was made of 30 plus five days added to make up 365 days. The five days were added after many calculations and we cannot disregard them. As there were no roz names left, we used the names of the Gathas for the five extra days.