Need to recover website's database from server backups

[XCore]

The domain for this website was deleted (in error) which also deleted the files and database.
I readded the domain and the database all with same names and paths.
I have the server backups which have the MySQL database files for the website. All the files are 'frm', 'MYD' and 'MYI' files. I have no idea how to restore the database from these files.
I have tried simply copying the files to the newly created database folder at '/var/lib/mysql/user_db' (same name as before the deletion) but many of the tables "don't exist" when I try to access them via phpmyadmin.

Any help is greatly appreciated.
- Plesk v12.5.30_build1205150826.19 os_CentOS 6
- MySQL 5.1.73-5.el6_6

Thanks!