If I understand your objective correctly, I think you have the hash table backwards. Use the md5sum as the key and push each file name that matches onto an Array of Hash. Something like this (untested):

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dumper;
##############

my $dir = shift @ARGV;
my %md5_2file;

opendir(my $dh, $dir) || die "Unable to Open the Directory $dir $!\n";
chdir $dir or die "Cannot Change to directory $dir: $!\n";

while (my $file = readdir $dh) {
    if (-f $file) { #takes care of ./ dir's and also no need to chomp(
+)
        my ($md) = (split /\s+/, qx(/usr/bin/md5sum $file))[0];
        push @{$md5_2file{$md}), $file;
    }
 }
closedir($dh);

foreach my $md5 (keys %md5_2file)
{
    print "$md5: @{md5_2file{$md5}}\n"; # md5: file2 file2 filen
    # this md5 is unique if ( @{md5_2file{$md5}} == 1) 
}
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