Howdy Wort,
I would love to help you with this. I bet I know why that table is so large. Did you have month view cache enabled at some point (setting located in WP-Admin > Events > Settings > Display ) ? It will cache any month a visitor goes to. Unfortunately certain tools, like those use to scan websites for vulnerabilities, will spider through many thousands of views on your website including month view. This can create a very large cache of wp_transients, each containing a month view. If you have 5000 in your database than it is likely something looked at about 400 years worth of months on your website, and each got cached.
The cache will clear itself after a while. You can tell it to stop making new entries by disabling month view cache. Further using a plugin like Transient Cleaner you clear all WP transients immediately if you don’t wish to wait. After this is done your site will either be running fast again or it was not this slowing you down.
Obviously this is not ideal. Normal robots obey the robots meta tag we have in place that tell them to stop spidering, but some like security scanners do not. We are looking into throttling the amount of entries that get created to prevent this sort of issue, and probably only cache months that are viewed frequently.
I am sorry to hear you server is running slow. If I can be of further help let me know. Performance is a huge passion of mine.
Cheers!
– Brook