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My primary MacOS partition got corrupted and I can not repair it or make it bootable.

Here's the breakdown of the situation: I had this MacOS Sierra partition, 450 GB, and a second partition with MacOS High Sierra, 50 GB. I booted as usual on Sierra and tried creating a new partition using Disk Utility by reducing the size of the 450 GB partition in 50 GB. The goal was to later enlarge the High Sierra one. The operation failed so I restarted, held CMD+R > Disk Utility and tried to First Aid my primary 450 GB partition. It failed as well.
The High Sierra one still boots fine but when I try to repair the Sierra partition, Disk utility gives me this message:

Repairing file system.
Volume is already unmounted.
Performing fsck_hfs -fy -x /dev/rdisk0s2
Checking Journaled HFS Plus volume.
Invalid number of allocation blocks
The volume   could not be verified completely.
File system check exit code is 8.
Restoring the original state found as unmounted.
File system verify or repair failed.
Operation failed…

Also, a new dummy partition called disk0s4 showed up with the exact same size of those 50 GB I tried creating on the first place. Disk Utility will not allow me to delete it.

Can you guys please help me out? I do believe this should be "easily" fixable via some sort of high level Terminal command.

sudo gpt -r show disk0 results:

       start       size  index  contents
      0          1         PMBR
      1          1         Pri GPT header
      2         32         Pri GPT table
     34          6         
     40     409600      1  GPT part - C12A7328-F81F-11D2-BA4B-
00A0C93EC93B
     409640  782652408      2  GPT part - 48465300-0000-11AA-AA11-
00306543ECAC
  783062048    1269536      3  GPT part - 426F6F74-0000-11AA-AA11-
00306543ECAC
  784331584   96124576      4  GPT part - 48465300-0000-11AA-AA11-
00306543ECAC
  880456160     262144         
  880718304   96124576      5  GPT part - 48465300-0000-11AA-AA11-
00306543ECAC
  976842880     262147         
  977105027         32         Sec GPT table
  977105059          1         Sec GPT header

sudo df:

Filesystem                        512-blocks      Used Available 
Capacity iused      ifree %iused  Mounted on
/dev/disk0s2                       782652408 712293504  69846904    92% 
1236092 4293731187    0%   /
devfs                                    390       390         0   100%     
676          0  100%   /dev
/dev/disk0s5                        96124576    306608  95817968     1%     
146 4294967133    0%   /Volumes/Untitled
map -hosts                                 0         0         0   100%       
0          0  100%   /net
map auto_home                              0         0         0   100%       
0          0  100%   /home
localhost:/oH1iUNq0m11UpXt--bqLKM  782652408 782652408         0   100%       
0          0  100%   /Volumes/MobileBackups
/dev/disk2s2                       253044736  23065088 229979648    10%   
90098     898358    9%   /Volumes/128 GB
/dev/disk1s3                         1269760   1101624    168136    87%     
215 4294967064    0%   /Volumes/HDM Recovery
/dev/disk1s4                       974759168 830544520 144214648    86%  
653486 4294313793    0%   /Volumes/ART
/dev/disk1s2                       975396824 704192064 271204760    73% 
1104809 4293862470    0%   /Volumes/CCC

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