Aside from the S.M.A.R.T. attributes initially indicating the warning, the Reallocated Sector count, the Current Pending Sector Count and the Uncorrectable Sector Count are very high, all point to a failling hdd.
As suggested, you could clone the drive. Macrium Reflect is a popular application which is easy to use. But looking at the number of Reallocated Sectors Count (2378) it is very possible that there would be a fair amount of file corruption. This would include your personal files as well. Unfortunately your attitude regarding backing up your personal files may come back to bite you right on your arse. If you decide to go ahead with Macrium Reflect there is a tutorial which you may find useful, you can find it here.
I would suggest that you use the computer only to backup your personal data. In the condition it is in continued use very possibly could cause a quicker failure of the drive.
Hopefully this experience will motivate you to back up all of your important data to removable media, such as an external hdd, flash drive, DVD, Cloud, etc.