Here is an information about automated backup for Azure MySQL
Is my Azure Database for MySQL server keeping track every five minutes of transaction logs?- Yes, here is snippet and reference link https://learn.microsoft.com/en-us/azure/mysql/flexible-server/concepts-backup-restore
If yes, is it saving it in a particular location?
By default, Azure Database for MySQL server backup storage is locally redundant for servers with same-zone high availability (HA) or no high availability configuration, and zone redundant for servers with zone-redundant HA configuration.
Let us know if you have any additional questions.