Hi I have an iMac from 2013 with the specs as follows:
3,1 GHz Quad-Core Intel Core i7, Turbo Boost upp till 3,9 GHz
16 GB 1600 MHz DDR3 SDRAM - 2 x 8 GB
1 TB Fusion Drive
NVIDIA GeForce GT 650M med 512 MB GDDR5
And it has the very latest MacOs with latest patch, upgraded last week.

However whan I started (tried) my iMac yesterday it started working and then just closed down..
I tried several times but started realizing something is wrong.
So I looked at google for help and has performed the following actions:

1. Start in safe mode Shift (⇧) = iMac still closes down without starting
2.Start with Command (⌘) and S opening black window where I enter fsck -fy = the system answered "The volume [iMac name] appears to be OK" = iMac still closes down without starting
3.Start with Command (⌘) + R opening recovery area. I tried disk utility "First Aid" and MacOS disk was OK, Fusion drive was OK but coming to MacIntosh HD it stated Not OK and something with:

"Fixing size of logical volume to fill logical volume group.The operation couldnt be completed. (com.apple.DiskManagement.disenter error 49153.) A disk with a mount point is required. Operation failed..."
4. Reset SMC removing acdc 15 secs then wait 5 secs before start = iMac still closes down without starting
5. Reset NVRAM by start with Command (⌘), Alternativ (⌥), P and R a number of times = iMac still closes down without starting
6. Reinstall MacOs via Start with Command (⌘), R = There is NO disc visible to install to at all (show all discs is on) = iMac still closes down without starting
7. Trying to reinstall to latest version that followed the iMac by Commando (⌘),Shift,Alt,R = iMac still closes down without starting
8. Trying to reinstall to latest compatible version of macOs by Commando (⌘),Shift,Alt,R = iMac still closes down without starting
9. Trying to use my timemachine backup Start with Command (⌘), R = There is NO disc visible to install to at all (show all discs is on) = iMac still closes down without starting

So as you can see I tried a lot of things...Did I miss anything that could help??? If so Please help out
Also noticeble is that when I start the iMac I can see the progressionslider going for a while and then I hear the harddrive shutting down and then the iMac goes black in shutdown.

So what do you think has happened??
Could it be (as I suspect) that my hardrive has died??
If so is it at all possible to fix and replace a hardrive when I have a fusiondrive??
Or is it simply not worth the effort??
And should I instead buy a new iMac with SDD disk only this time??? (I assume a SDD is safer)

Is it common that the hardrive dies?? I had this iMac since january 2013 so its approaching 5 years but stil not so old...

Please help out and any comments feedback is extremely appreciated..
best regards Micael