Five billion is a big number. If you combine the populations of the top 10 most-populated countries on Earth, you get less than that number. The best-selling game console of all time, the PlayStation 2, only sold enough units to cover 3.2% of five billion. Google Play Services has now passed five billion downloads on the Play Store, becoming the first app to do so.
If you're not familiar with how the Play Store works, it's important to note that Play Services hasn't actually been manually downloaded that many times. When someone logs into an Android device with their Google account, Google Play marks the pre-installed apps as downloads. So in reality, this means over five billion devices with Play Services installed were used at some point.
This lines up with Google's claim made at Google I/O, where the company said there were two billion active Android devices. It's not clear if Google's claim was only counting devices with Play Services, because there are many more phones and tablets without Google's suite of software (especially in countries like China).