recent photos taken on iPhone aren't going to desktop
recent photos taken on iphone aren't going to desktop Mac
iPhone 5s
Are you using My Photo Stream?
Make sure you are closing the Camara.app and do not keep it running in the background. The iPhone 5s likes to keep all apps running in the background, unless you really quit them.
The upload to Photo Stream will only start,
- when the camera is closed,
- when you are connected to Wif-Fi,
- and when your iPhone is properly charged.
Other than hat, check the settings, as described here: iCloud: My Photo Stream troubleshooting