cd /path/to/dir
touch now$$ # create a reference file
sleep 300 # wait for files to arrive
find . -newer now$$ -exec whatever_cmd {} \;
You can include other find search criteria e.g. a name pattern. Or in a loop, touch the ref file at every end of the iteration (before going to sleep).
cd /path/to/dir
process_all_files (find . -exec...)
touch now$$
sleep 300
while true
do
process files (find . -newer now$$ -exec...)
touch now$$
sleep 300
done
If you want this script to be restartable, perhaps you need a fixed ref-file name instead of "now$$", which would change on every invocation of the script (PID changes).
You take it from here.
HTH,
p5wizard