For context, a patent is being based on a paper I coauthored with my former post-doc advisor in graduate school five years ago (i.e., I was first author, he was the last author). I just learned that he filed it for a patent in late 2007 with only himself named as an investor and the application is about to grant. Is there anything I can do to assert my rights at this point?
If the patent was filed in 2007, and your joint paper was written 5 years ago (=2008 or 2009), then I would assume that you had no input on the actual patent -- the patent was written first.
Instead, your partner may have included material from his patent into your joint paper -- and if that is the case you would not have any rights to any part of his prior invention, especially since he filed the patent prior to writing your joint paper.
The only way this (you not being included as an inventor) would be proper is if the only aspects are claimed are aspects that were conceived by the other person. An inventor (don't think author = inventor, they are completely different concepts) is someone who made a conceptual contribution to something claimed in the patent. If you conceived of X and the other person conceived of a related Y (that isn't a special case of X) then a patent that only claims Y has only the other person as an inventor.
If that is not the case then you should be named as an inventor by law. What benefit that would convey to you is a separate issue.