Your use of the bareword SOCKET should be my $socket. Don't forget to declare your subs.

#!/usr/bin/perl

BEGIN {
    $|  = 1;
    $^W = 1;
}

use strict;
use warnings;
use Socket qw/PF_INET SOCK_STREAM inet_aton sockaddr_in/;

my $port  = shift;
my $proto = getprotobyname('tcp');
my $iaddr = inet_aton('172.16.1.5');
my $paddr = sockaddr_in( $port, $iaddr );

socket( my $socket, PF_INET, SOCK_STREAM, $proto )
  || die "Cannot prepare socket: $!";

eval { 
    die "Can't connect to $port" 
      unless connect( my $socket, $paddr ); 
};

shutdown($socket, 2);
sleep 1;
exit 0;
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