my @rows;
my @this_row;
my $num_per_row = 5;
my $in_this_row = 0;

while ( my $item = $sth->fetchrow_hashref ) {
    push @this_row, $item;
    if ( @this_row >= $num_per_row ) {
        push @rows, [ @this_row ];
        @this_row = ();
    }
}
[download]

At this point, you have an AoAoH (array of arrays of hashes). You could now pass this to a Template Toolkit snippet that looks something like:

[% FOR row IN table %]
<tr>
    [% FOR item IN row %]
    <td>item.id item.filename item.title</td>
    [% END %]
</tr>
[% END %]
[download]

And you'd end up with something very close to what you have, output-wise. I've left limiting the number of rows to 5 and linking the two snippets as exercises for the reader.