iPhoto deleted, need it for Mac 10.9.5

Apple stopped selling iPhoto. You cannot download installers for older versions, only updaters.

But the Updater to iPhoto 9.5.1, the version you need for Mavericks, is not available on Apple's download page. It has only been available from the App Store.

Is iPhoto listed in your Purchase history at the AppStore? On the fourth tab "Purchases"?

Yes, iPhoto from 2012.

Is there an "Install" button beside iPhoto at the AppStore? Then use it.

If not, you can only install iPhoto, if you upgrade your system to El Capitan. Then you can install iPhoto 9.6.1 from your Purchases history. But it is only compatible with OS X 10.3 or later.

Make sure there is no iPhoto.app anywhere on your boot drive or any external HD. Unmount the EHD if there is one there and then go back to the App Store and check again.

Did you reload the Purchased tab ? Enter ⌘R.

Search with the Finder for iPhoto. You may have accidentally dragged it to a different folder instead of deleting it.

• Open a Finder window and press the key combination ⌘ F for "Find".
• Type iPhoto into the search field.
• use the rule "name " is iPhoto.
• click "+" to add a rule "Kind is application".
• Set "Search" to "This Mac".

You should now be seeing something similar to the screenshot below.

If you select one of the search results, the path bar below the window will show you the folder where the item has been found.

if iPhoto is really not there but the appStore is seeing it as installed, rebuild the spotlight index as described here:

Rebuild the Spotlight index on your Mac - Apple Support

https://support.apple.com/en-us/HT201716

Another way to assure there's no hidden iPhoto app on your hard drive is to download and run Find Any File to search for a file named "iPhoto.app" as the file name.

FAF can search areas that Spotlight can't like invisible folders, system folders and packages. If there's an iPhoto.app hiding somewhere on your hard drive FAF will find it.