Is iPhoto in your list of previous purchases at the App Store? If you previously have been running Maverick, years ago, you may have associated iPhoto with your AppleID at the AppStore and can still download it. I am still seeing iPhoto in my previous purchases, when I open the Purchases view at the AppStore, and it can be reinstalled, but not purchased.
If yes, and iPhoto is listed at the AppStore with a purchase date, try the old stand-by to reinstall from the AppStore:
- Quit the AppStore
- Move your current iPhoto.app to the trash (don't empty the Trash),
- Then open again the fourth tab at the AppStore with your previous purchases and sign in with your AppleID
- Then click the Install button next to iPhoto to download and install it.
For OS X 10.9.5 Mavericks you would need iPhoto 9.5; the version I am still seeing at the AppStore for reinstalling is iPhoto 9.6.1, the compatibility update OS X 10.10.3, but if you are lucky (i cannot test it) the AppStore will offer you an iPhoto 9.5 version for your Mavericks system.
But I could still redownload it, even on macOS 13 Ventura:

None of the download links at Apple - Support - Downloads are for iPhoto versions compatible with your system version. They are for MacOS 10.7 Lion or earlier.