sling-shot
Wise Old Owl
I suggest you use this tool to take a backup to a new large drive so that at least your important personal files are saved. This will copy whatever is possible skipping any unrecoverable files behind.
FreeFileSync
After that on those pesky files which could not be copied you can try Unstopable Copier, a utility from Roadkill.net (I have not personally used it with Windows 10 yet) by keeping settings such that it will skip only the error filled sector after 1 try. After you have extracted whatever you can with this setting, you can try multiple effort settings so that it will try the maximum to recover any bad sector.
Roadkil.Net - Roadkil's Unstoppable Copier Program Download
FreeFileSync
After that on those pesky files which could not be copied you can try Unstopable Copier, a utility from Roadkill.net (I have not personally used it with Windows 10 yet) by keeping settings such that it will skip only the error filled sector after 1 try. After you have extracted whatever you can with this setting, you can try multiple effort settings so that it will try the maximum to recover any bad sector.
Roadkil.Net - Roadkil's Unstoppable Copier Program Download