Should be rather easy as almost all designs like that are the same. Some screws take the plastic shroud off which reveals the heatsink and heat plate. Should only be 4 screws behind the GPU that hold the heatsink on. You can then clean the plate and fan off of dust, then the heatsink while it's off. Use rubbing alcohol and qtips or a coffee filter to completely clean both the GPU and heatsink off of paste. Put a small grain of rice sized dab of paste on the GPU itself and carefully place the heatsink on to be mounted. That's all there is to it.
All of that is assuming you have a reference designed 5870.
Edit: Scratch that disassemble part. The heatsink, shroud, and plate all come off at the same time apparently for that card. You can refer here on what to expect. The rest is the same though.
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