It all depends.
If there was partitioning done on the drive, and it's not the first partition that you need data off, chances are good you'll be able to recover your data, since it'll still have all it's filesystem data, just no reference to where the partition starts. (As this information is stored in the MBR.)
In the case of no partitions or the first partition holding the data you need, you're going to be in a lot worse shape.
Being that 5% of the drive most likely is well past any inode/FAT/whatever tables, it may become very difficult to identify what on the disk is data, where files start and end and what is garbage. How much of this information can be recovered depends on the filesystem you used on the partition and in some cases how it's configured.
But even when none of this information can be recovered, all is not lost. It is possible to just traverse the entire drive/partition and look for certain signatures that denote specific file types. Without going into too much detail, this obviously requires speciality software with intimate knowledge on the type of file and filesystem you want to recover.