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If you only need to show these 5 zip codes once, one option is to:
Drag zip codes to your label mark,
Highlight all data points on your map (Ctrl + A),
Right click a random data point and select "Mark Label" -> "Never Show"
Select the 5 zip codes you need, right click one of the zip codes and select "Mark Label" -> "Always Show".
Thank you - that's exactly what I was trying to do and that was a quick way to do it.