Well you can't do it with the cron job but you can use the cron job as an initiator.
This could be a way to solve this issue. you can run a cron job everyday at 13:00 o'clock.
Your script on the other hand should have a loop which sleeps 5 second and goes again through the loop. Once you reach 17:00 o'clock it will stop the loop and exit.
And there should be another check in the loop, which checks whether you are between the given time e.g. 13:00-14:00 or 16:00-17:00, if so it will run your script and sleep 5 seconds, if not it will just run the the loop
Another way would be to run a cron job every hour.
And in your script you have to check it the hour is the one you want to start doing something. if so, you just do it like the above loop.
Credit to: litux