I think what you want is to clone the drive. I can't recall if it is possible to clone to a partition rather than a drive but you are better off just copying over everything important to you and just doing a fresh OS install and dealing with reinstalling programs and drivers, steam games and such can easily be backed up to the external drive through their respective platforms so no worries about that.
As a note on safely backing up your drive, it doesn't exist, the sheer act of stressing a failing drive to try and save the data will likely cause a catastrophic failure, this is why raid 5 sucks. I would move your most important files first, then proceed with the data that can be replaced followed by data that can be easily replaced. Between bitrot, read andwrite errors and total drive failure you rarely save 100% of a dying drive but that doesn't mean you can't maximize the chances of saving the data that matters.