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I just downloaded 5.1.1, which came with a version of DXCC.rsd

I have 5.1 already on my computer, and the DXCC.rsd file in that folder contains edits I made over time.

Is there a way to merge the two files? Copying my existing DXCC.rsd file to the 5.1.1 folder is an option, but there may be data in the 5.1.1 DXCC.rsd that is not in mine.

73,
-jav k4jh

Keep your old file.
All entries added in the new version can be imported/merged using the "Download" option in the "EditDXCC" application.
It is also recommended to use the K7PT service for downloading the irregular call signs and dx-pedition plans. This will update your dxcc.rsd automatically. See the General tab in the RUMlog preferences.

OK, I see the check box to use the K7PT service, I checked it. When does it download updates? Upon RUMlog start?

K7PT provides an update every day. RUMlog looks for new data at start up. See page 66 of the manual.