When Ed Morton posts an awk solution it is usually a small tutorial for low level users like me...
But in any case since i have been working on this exercise for the last hour and a half, i thought to take my risk to post this solution which is a transformation by the link you already found
$ awk '$0 ~/<film.*>/{++delim} {file = sprintf("chunk%s", int(delim/7)); print >file; }' file4
Testing:
I used a small bash loop to create a small film file with 50 records and split those films by 7 for testing:
$ for ((i=1;i<50;i++));do echo -e "<film$i>..............</film$i>" >>file4;done
$ head file4
<film1>..............</film1>
<film2>..............</film2>
<film3>..............</film3>
<film4>..............</film4>
<film5>..............</film5>
<film6>..............</film6>
<film7>..............</film7>
<film8>..............</film8>
<film9>..............</film9>
<film10>..............</film10>
$ awk '$0 ~/<film.*>/{++delim} {file = sprintf("chunk%s", int(delim/7)); print >file; }' file4
$ cat chunk0
<film1>..............</film1>
<film2>..............</film2>
<film3>..............</film3>
<film4>..............</film4>
<film5>..............</film5>
<film6>..............</film6>
Another test in which each film has some newlines:
$ for ((i=1;i<50;i++));do echo -e "<film$i>...\n...\n...\n.....</film$i>" >>file4;done
$ head -n20 file4
<film1>...
...
...
.....</film1>
<film2>...
...
...
.....</film2>
<film3>...
...
...
.....</film3>
<film4>...
...
...
.....</film4>
<film5>...
...
...
.....</film5>
$ awk '$0 ~/<film.*>/{++delim} {file = sprintf("chunk%s", int(delim/7)); print >file; }' file4
$ ls chunk*
chunk0 chunk1 chunk2 chunk3 chunk4 chunk5 chunk6 chunk7
$ cat chunk1
<film7>...
...
...
.....</film7>
<film8>...
...
...
.....</film8>
<film9>...
...
...
.....</film9>
<film10>...
...
...
.....</film10>
<film11>...
...
...
.....</film11>
<film12>...
...
...
.....</film12>
<film13>...
...
...
.....</film13>
Well, in both cases seems to work ok. Mind that in this configuration input file is splitted per 7 films - not per 7 lines. You can change this number to whatever.