That said, I don't know how you would obtain a list of hashed passwords without also getting the associated list of salts (wouldn't they be in the same database?), so it is kind of a moot point. The different salts are intended to prevent against the ability to have a single rainbow table to crack every password in the database.
Instead, you need a table for each salt, which means that you basically have to brute force the entire database. This still doesn't really help if you are using something fast like MD5, as brute force solution will be possible with that algorithm. Which is why you want something reasonably slow.