According to your table, "Sharks" has the sub-categories "Small Critters" and "Sharks"(!). That doesn't make sense. Both should probably be subcategories of "Salt Water".

The typical representation in Perl of a tree like yours would be a hash of arrays. Keys are the category names and values hold the list of corresponding sub-categories. Leaving all database issues aside, I'll assume (a corrected version of) your table is presented as a text file. The following code builds the tree hash %tree from the data. The sub print_tree then prints an indented table of the categories.

my @names;
my %tree;
while ( <DATA> ) {
    chomp;
    my ( $id, $parent, $name) = (split ' ', $_, 5)[ 2, 3, 4];
    $names[ $id] = $name;
    if ( $parent ) {
        push @{ $tree{ $names[ $parent]} }, $name;
    }
}

print_tree( 'Animals', \ %tree, 0);
exit;

use constant INDENT => '    ';

sub print_tree {
    my ( $root, $tree, $level) = @_;
    print INDENT x $level, $root, "\n";
    for ( @{ $tree->{ $root} } ) {
        print_tree( $_, $tree, $level + 1);
    }
}

__DATA__
        Edit    Delete  1       0       Animals
        Edit    Delete  2       1       Mammals
        Edit    Delete  3       1       Fish
        Edit    Delete  4       2       Dog
        Edit    Delete  5       2       Cat
        Edit    Delete  6       3       Fresh Water
        Edit    Delete  7       3       Salt Water
        Edit    Delete  8       7       Sharks
        Edit    Delete  9       7       Small Critters
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Anno