Is the Khums year based on the 12 month Gregorian calendar (365 days) or the 12 month Islamic (hijri) calendar (355 days)?
A person can choose to calculate his/her income based on the Islamic lunar calendar or the Gregorian solar calendar for Khums.
1775. A person can pay Khums as and when he/she earns a profit during a year, and it is also permissible to delay payment of Khums till the end of the year. And there is no objection if one adopts the solar year for the payment of Khums.
https://www.sistani.org/english/book/48/2286/