Lollipop 5.1, completely safe from stagefright?
You can use Zimperium's Stagefright Detector app to test your device for the known attack vectors. The bugs were not patched upstream until Android 5.1.1, but it is possible (particularly based on the change notes) that Motorola backported security fixes to their 5.1 release, so the version of Android you have is not necessarily the best indicator.

NB: One of Zimperium's researchers is Joshua Drake, who disclosed the Stagefright vulnerabilities to Google and submitted patches to fix them. It is therefore reasonable to conclude that the tests in their app are more than likely accurate.