My Hard disk stopped working on mac

So I have a 21.5 inch İmac mid 2011.Its a Mac OS X Lion 10.7.5. So I bought this hard disk (Samsung 500gb ST3500) a year or two ago and then did the correct formatting so it could run on the mac.This summer I took it off my mac for about a month and now I felt like listening to Wilko's Yankee Hotel Foxtrot and realized it was on the hard disk so I put it back on and now its not showing up? It was fine before.

I tried going in disk utilities and it shows up there so I verified it and although it didn't notify me for any repairments I still clicked on repair and it didn't help.Theres a lot more info there then just that album, a whole lot of great movies , tv shows and a big library of great music that I was looking forward to get back into, as well as a couple programs also plug ins for my ableton , so now I cant open up my projects either. So I really don't wanna format it.

Any help will be greatly appreciated , theres a lot of info on this hard disk.
 
In Disk Utility, does the disk show a partition? If so, highlight that partition, and then in the bottom left of that window there will be a blue clickable 'link'. Click that.
 
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