The simplest way is to synchronize the clock of the Pi with your RTC and simply use cron. Depending on how much your pi diverges, you can sync the clock of the pi from time to time in cron too.
Typically, that would look like :
#M H dom mon dow cmd
0 * * * * rtc-pi
0 12 * * * script_to_turn_on
5 12 * * * script_to_turn_off
--- addition---
For those that have a DS1302, it may be obvious that rtc-pi is the program that interfaces with the DS1302 module. It is not in the standard repositories, but can be obtained from (among others) https://zedt.eu/storage/2014/07/rtc-pi-20140727.zip. For other versions of the RTC (like the DS1307) the command would be hwclock, which can be downloaded from https://github.com/Seeed-Studio/pi-hats.git