Typically, when the year is the same, the license is the same. In this particular case, it is NOT the same. Inventor Publisher 2013 is not the same as Inventor Publisher 2013 R1. This means that you will need a different serial number and product key for Inventor Publisher 2013 R1 when installing it.
In the example below, a -5 error means that there is no FEATURE on the license server for the Autodesk product.
Thanks to John Weiss for confirming this is indeed the issue.
Reference
http://usa.autodesk.com/getdoc/id=TS17838085
Epilogue
The product key for Inventor Publish 2013 R1 is 666E2.
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