I don't know what the procedure is on a Samsung GS5 phone, but on my Nexus 5, the way that Play Services gets updated is when updating an app that requires an updated version of Play Services. The system will then put up a notification saying that "Such and such app needs an updated version of Google Play Services". Upon tapping on the notification, the Play Store opens to the Update page for Google Play Services. Then you can press the Update button for it and it will update like any other app.
After that, the original app that needed the update can be updated like normal.
Doing a search for Google Play Services in the Play Store will not find it. It's a special system-level app. As far as the version numbering goes, I believe it may vary depending on the device, at least in terms of build number. For example, my Nexus 5 has Play Services version 7.3.29 (1866531-438). My Verizon LG G3, which was just updated to Android 5.0, has 7.3.29 (1866531-430). On the G3, the update to Play Services didn't appear until several apps demanded it (Hangouts, in particular) after Android 5.0 was installed. (I don't know what version of Play Services it had prior to Lollipop.)
The differences in build numbers is reason enough to NOT try to side-load Google Play Services from sites like Android Police. There's no telling what device- or carrier-specific differences there are, and it's possible that some of the flaky behavior that some users get on their phones is the result of past side-loading of the wrong version of that special system app.
P.S. Keep in mind, we're talking about "Google Play Services", not the "Google Play Store" app. For reference, my Google Play Store app is at version 5.4.12.