How do I enable GPU rendering?

I am using Ubuntu 18.04, I use blender 2.79, and my GPU is an ATI Radeon HD 5870.

I am really hoping someone here can help me with setting up GPU rendering. I have installed many different libraries, but I still cant get blender to recognize my GPU.

Can someone please help? I would really appreciate it. Thank you!

Take a look at this:

This is a quote from the Blender Manual:
OpenCL is supported for GPU rendering with AMD graphics cards. (We only support graphics cards with GCN architecture 2.0 and above).

From my understanding the Radeon HD 5870 does not meet the GCN requirement. Or in other words: That card simply is too old.

The radeon RX 460 will blast that card away.

Upgrade your radeon software.