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I regret to inform you that it is not possible to recover all of the deleted emails in the period of last 5 years.
But, you can try the following to check how many of them it can recover:
Please login into your Hotmail/outlook.com(now, it is renamed as outlook.com by Microsoft).
In the left pane of the Outlook.com window, click the Deleted folder. At the bottom of the window, click recover deleted messages.
Outlook.com will recover as many messages as possible and put them in your Deleted folder. If you don't see the deleted messages that you wanted, it means they are permanently lost.
When the recovered messages are back in your Deleted folder, you should move the important ones back to your inbox or personal folders because the Deleted folder gets cleaned out periodically.
You can find this information under this page:
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