DBI is the plumbing; DBD::mysql is the fitting. You need both.

From the doc for DBD::mysql (plus your error handling):

my $dsn = "DBI:mysql:database=$database;host=$hostname;port=$port";
my $dbh = DBI->connect($dsn, $user, $password) or die "Couldn't connec
+t to database: ".DBI->errstr;
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Set up all those variables then use that exact code snippet and it should work for you.

Hope this helps!