use warnings;
use strict;
use Integer::Partition qw();

my $i = Integer::Partition->new(6);

while (my $p = $i->next()) {
    print join( ' ', @$p ), $/ if (@$p == 5) and not all_same(@$p);
}

sub all_same {
    my $same = 1;
    for (@_[1 .. $#_]) {
        if ($_ != $_[0]) {
            $same = 0;
            last;
        }
    }
    return $same;
}

__END__

2 1 1 1 1
[download]

Or, if all the values of the partitions must be unique, maybe something like (untested):

use Integer::Partition qw();
use List::MoreUtils qw(uniq);

my $i = Integer::Partition->new(6);

my $n = 5;

while (my $p = $i->next()) {
    do_whatever_with($p) if (@$p == $n) and (@$p == uniq @$p);
    }
[download]

That MoreUtils module seems to be really handy, but I tried some bigger numbers & I might have to rethink the overall approach. Thx for the help though everybody.

That works to give me the exact number of summands I'm looking for but it give me repeat summands. I get the idea behind the subroutine but I'm not sure how to change it so that it gives only partitions with distinct summands. I tried tinkering with the truth values & the != etc but it didn't seem to do the trick.

In Perl, "distinct" means "hash":

sub distinct {
    my %distinct;
    @distinct{@_} = ();
    return keys %distinct;
}
[download]

لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ