Some (many) hosts won't let you do this. They simply won't give you access to the data directory - you're not the only person with files in there. It would only work if you have exclusive access to a data directory for the MySQL server. Check with the hoster for details.
To solve this, do a dump of your tables and run the dump files on your new hoster. If the new hoster hasn't got PHPMyAdmin, you can install it yourself in most cases. It's not a security risk for the hoster and the hoster's other customers.
Best o luck
Norm