If you look at the synopsis of the DBD::mysql docs, you can see the extended form of the connect string there:

$dsn = "DBI:mysql:database=$database;host=$hostname;port=$port";
$dbh = DBI->connect($dsn, $user, $password);
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People usually use the short form "DBI:mysql:$database", but that won't work in your case.

The port number is still optional.

More options still are listed under the heading "connect".