Hi onesickpuppy, and welcome to Piriform.
I can understand and sympathise with the username. This type of thing sucks. You're not the first and you won't be the last to make a simple but pretty consequential slip up. Try not to beat yourself up.
I have never formatted an NTFS drive (and I assume that's what we're talking about here) to Linux so have no idea how that process works, but if the time involved wasn't much more than the 5 minutes you mention then I doubt that a full format of the drive was carried out.
One of the other guys who've possibly carried out this type of file format change to a drive may have a definitive answer to the point I'm raising, and that is it may be possible that only the initial boot sectors of the drive have been changed to reflect the new file system, and the data may still be there.
Have a read here, and you'll understand why I'm thinking that way ...
Solved: Mistakenly changed my main NTFS Partition to EXT4. Data gone?
And this is the free software used ...
PhotoRec:
Photrec is file data recovery software designed to recover lost files including video, documents and archives from hard disks, CD-ROMs, and lost pictures (thus the Photo Recovery name) from digital camera memory.
PhotoRec ignores the file system and goes after the underlying data, so it will still work even if your media's file system has been severely damaged or reformatted.
Photrec may look like command line and simple, but it is menu driven, very powerful and has extensive help files and guides so is well worth the effort of getting to know.
Try this first, but you may also be able to get at your data (if it's still there as mentioned above), by using a "LiveCD".
The LiveCD List:
An example of how to use a LiveCD here, and a good one at that ...
How to use an Ubuntu LiveCD: (How-to Geek)
Hope that helps, and you may get some input from one of the other guys if they have experience with this. And of course post back if you need enlightenment on any of the above.
We may not have it but we'll try our best.
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