Outlook's storage limit is separate from the overall storage provided by Microsoft 365. The 5 GB limit you are encountering is likely due to the storage quota for your Outlook mailbox itself, which is different from the 1 TB of OneDrive storage included with your Microsoft 365 subscription. To manage your mailbox storage, you may consider enabling an archive mailbox or using retention policies to automatically delete or archive older emails. This will help in managing the size of your mailbox and prevent it from reaching its limit.
References:
- "Mailbox is full" warning even if the mailbox hasn't reached the storage limit
- Status bar progress never shows more than 3.99 GB remaining on initial Sync of large folders
- "(Message store has reached its maximum size) error when a Microsoft 365 user tries to delete an item in Outlook or Outlook on the Web"
- Increase the Recoverable Items quota for mailboxes on hold