Google officially supports the Assistant only on devices with Android 6.0 or above. If you have an Android 5.0 Lollipop phone however, you are out of luck. However, there is a workaround.
XDA Member Nikhilkumar038 has demonstrated a way to get the Assistant on Android 5.0 phones, without the root access. The workaround involves using the Beta version of the Google app, and also the Nova launcher. You cannot however launch the Assistant from any screen or by long pressing the home button without installing it as a system app. For that, you will need root access.
If you are ready to live with that little inconvenience, you can enable Assistant on your Lollipop phone or tablet right away. Here is a video explaining how to do this:
If you prefer step by step instructions, head over to XDA Developers blog here. After getting Assistant on your phone, do not forget to subscribe to this blog for regular updates and tips!