my @dirs = (
    '0555-DDBB/AirPhotos',
    '0555-DDBB/AirPhotos/AP Labels',
    '0555-DDBB/AirPhotos/new database',
    '0555-DDBB/FOO M',
    '0555-DDBB/FOO M/0555-055-01 Site/Photos',
    '0555-DDBB/FOO M/0555-055-01 Site/Photos/Digital',
    '0555-DDBB/FOO M/0555-055-01 Site/Photos/PhotoList',
    '0555-DDBB/FOO M/0555-055-01 Site/Reports/Summary',
    '0555-DDBB/FOO M/0555-055-01 Site/Reports/Daily',
    '0555-DDBB/FOO M/0555-055-02 Design',
    '0555-DDBB/FOO M/0555-055-02 Design/photo',
    '0555-DDBB/FOO M/0555-055-02 Design/photo/Ortho',
    '0555-DDBB/FOO M/0555-055-02 Design/Correspondance',
    '0555-DDBB/FOO M/0555-055-02 Design/Drafting',
    '0555-DDBB/FOO M/0555-055-02 Design/Drafting/DWG',
);

use strict;

my %tree;
for my $d (@dirs) {
    my $n = \%tree;
    $n = ($n->{$_} = exists $n->{$_} ? $$n{$_} : {})
        for split('/', $d);

}

print_tree(\%tree, 0);

sub print_tree {
    my($tree, $indent) = @_;
    for(keys %$tree) {
        print " " x $indent, $_, $/;
        print_tree($tree->{$_}, $indent + 1)
            if ref $tree->{$_} and keys %{$tree->{$_}} > 0;
    }
}

__output__

0555-DDBB
 AirPhotos
  AP Labels
  new database
 FOO M
  0555-055-02 Design
   Drafting
    DWG
   photo
    Ortho
   Correspondance
  0555-055-01 Site
   Reports
    Daily
    Summary
   Photos
    Digital
    PhotoList