Is it possible to stream from Safari to Apple TV with a MacBook Pro late 2008 with OS X 10.9.5?
Unfortunately, the graphics card in your Mac doesn't support AirPlay as its too old. I have the same problem with my mid-2010 MBP. You can see the list of supported hardware here.

While there is software that will enable this functionality (like AirParrot), I have found it severely under performs on older hardware and isn't really usable. You're welcome to give it a go though. :)