You can backup the ESM5_2 database (Archive database) and restore it on the new server, then install ESM as an update over that database.
However, the only way to keep access to the old archive footage would be if you moved the video over to the exact archive server volume path including library items. (for example if you are currently recording to D:\Archives\, you would move all the video over to the same path, D:\Archives\).
If this is not an option and you will be recording to another archive server volume path, you have the option of keeping the old server volume linked to the management server but disabled the cameras and put the server volume to null so it doesn't spin up the server capture processes. If you need to review footage, you can do so by enabling the camera so it shows back in the user interface temporarily on the old server until the retention period expires.