Good evening Julie and welcome to the Events Calendar Support forum!
Thank you for reaching out to us and for sending us your system information.
We are sorry to hear about the issues you are having with recurring events.
I would love to help you with this topic.
Based on your profile, it looks like you are several versions behind on both the Events Calendar plugin and the Events Calendar Pro add-on.
Before attempting anything, I would highly recommend a backup of everything.
If you are not quite ready to fully upgrade, at the very least, you might want to use a matching version of Pro by downloading it from your Downloads page. In this case I would recommend version 4.0.1
Finally, as a side note, although PHP 5.3.10 will work fine in most cases, it is worth knowing that officially WordPress recommends version 5.6 and above.
Let me know how that goes.
Best regards,
Geoff B.