First of S.M.A.R.T data is a bit of a mixed bag. It tends to be not outstandingly accurate / reliable. It is just reporting what the disk says. It is not asking any questions. It is useful as a warning sign.
Bad blocks doesn't always equal to lost data. Disks don't just write data and pray that never ever something goes wrong. The data is protected by forward error correcting codes and in many cases can be recovered from a bad block and moved. You can first try boot a linux distro and and us bad blocks command or use the tool packaged with windows for drive analysis and repair. Th badblocks command would be:
badblocks -vs /dev/sd#
Where # is the drive number. I would recommend booting a linux and us bad blocks since it is usually better to do this while the drive is not in use.
These tools are fine for a first try. If they fail there are more sophisticated solutions. My trusted one for years has been SpinRite. It is not open or free but it is very affordable and has been around for years. I would not use it to "resurrect" disks for prolonged us as people tend to do, but it is very useful for data recovery and the price is right. If your data is precious to you it might be worth spending the 90 bucks go give it a try.
And for the future ( I am sorry but I have to stress this ), do make regular backups. It is not paranoid to do so. When done properly it is very cost effective counter measure to many problems. Disk failure, theft, fire, human error and even many types of virus infections. Take a regular full system backup (once you made major system changes or quarterly, you only need the most recent one) and make daily (if you are brave weekly) backups. If stuff hits the fan you can be back to normal within 30 min.