It is a very common situation when your company uses an Exchange 5.5 server, running on old hardware. The server is reaching the end of its life while funding for a major upgrade project is pending or not available.

In this 10 Step tutorial we will show you how to move your Exchange 5.5 resources to a new hardware. This approach is suitable when your existing server is still running so you can introduce the replacement as an additional Exchange server in the same Exchange organization.

If your existing Exchange 5.5 server is not available (i.e. it crashed or is not able to mount the stores) then you should take a look at the second screencast in this section
Moving Exchange 5.5 to new hardware - restoring the Exchange 5.5 to different hardware using Online/Offline backup .