Can I use a Tamron AF 70-300mm f/4.0-5.6 Di LD Macro Zoom Lens on the LA-EA1 adapter for my nex5 camera?

I bought a Nex5 camera but can't afford to buy the Sony e-mount telefoto lens. Anyone can tell me if I can use the above lens with the Sony LA-EA1 adaptor for Sony A mount lens? Can this lens be used in auto focus mode with the adapter?