Recovering data from a hard drive with too many bad sectors

Thanks @jumanji

Regarding the hard drive. It was not part of the PC. I bought it a few years before the PC and was using it to store some of my files. So it wasn't connected to anything most of the times, just sitting in my drawer.
Following your instructions, I took a screenshot of the disk management. One thing to note here is that when I turn the hdd on, it will show up in the disk management but the window becomes non-responsive.


And here is the screenshot of Partition Wizard.

just saying, I would make an image of the disk and work on that....

There seems to be a lot of mixup here and which I am unable to decipher.. You say that you bought the 500GB HDD even before you bought the Desktop ( which your wife is using now) and was using the 500GB HDD for storing the data. But the Windows Disk Management screenshot shows that it was a system disk on a PC with UEFI Bios..

We don't know any details of your laptop to which it is plugged in now but I guess it has a standard bios. The two highlighted partitions seem to be in an extended partition with two logical drives which may be your data partitions.

I would think it is necessary now to remove the active flag from the EFI System partition on the 500 GB HDD. We can't do anything with Disk Management since it has become unresponsive. Can't do anything with PW since it is as confused as I am and hence throws up a bad disk message.

I would in this case solicit the opinions from other Windows10 experts like Bree, dalchina, topgundcp and others - the list is long that I can't mention everyone. Let us wait and see as I continue to brood on this. .

These are trial and error steps:

1) Find a flash drive that you can format

2) On a working computer create a bootable Ubuntu flash drive:
Create a bootable USB stick on Windows | Ubuntu

3) Read this link:
(Recover files from a failing drive)
Linux to the rescue! How Ubuntu can help a computer in distress | PCWorld

3) See if you can recover data