You are computing every distance twice. It probably is better to keep your results in an array and take advantage of symmetry.

use strict;
use warnings;
use Data::Dumper;
my @data;
while (<DATA>) {
    next if !/\S/;
    push @data, [split];
}

my @array;
for my $i (0..$#data) {
    $array[$i][$i] = 0;
    for my $j ($i+1..$#data) {
        $array[$j][$i] = $array[$i][$j] = distance( $data[$i], $data[$
+j] );
    }
}
print Dumper( \@array );
 
sub distance {
    my ($p1, $p2) = @_;
    return sqrt (
          ($p1->[0] - $p2->[0]) ** 2
        + ($p1->[1] - $p2->[1]) ** 2
        + ($p1->[2] - $p2->[2]) ** 2
    );
}
__DATA__
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
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