There's nothing to stop you putting two cron job entries; one for the first hour's schedule and a second one for the rest of the day. You can call exactly the same script in both.
This is quite simple unless I've missed something somewhere?
5-59 0 * * * <full path to script>
0-59 1-23 * * * <full path to script>
First entry schedules the first hour
Second entry hours 1 thru' 23
NOTE: This schedules every day, ie,7 days a week.
If you're new to cron also note that you must set all variables needed in your script. Cron knows NOTHING about variables set on interactive login such as those set in .profile.
Ideally, DON'T edit crontabs directly otherwise you may need to wait up to 24 hrs for the job to run.
Use the proper crontab tools if you can.