The filehandle will be closed when you open it again so you don't have to do that explicitly.

Here is a variation:

    perl -ne '$n=$.-1; open F, ">$n.txt" unless $n%5; print F' file
    
    Creates:
    0.txt
    5.txt
    10.txt
    ...
[download]

This omits IO checking for the sake of a one-liner.

Here is a slightly longer one but with better output filenames:

    perl -ne 'BEGIN{$s="file000"} open F, ">". $s++. ".txt" unless ($.
+-1)%5; print F' file

    Creates:
    file000.txt
    file001.txt
    file002.txt
    ...
[download]

Although, realistically I'd use split for this task as shown by tirwhan above.

--
John.