This seems simple enough… but I had to try a few methods to get it right.
Note: the solution here is the one I settled on because it’s the first one that worked for me. There probably are better solutions available. Feel free to comment if you have any.
I settled on using Notepad++, my go-to text editor. It has a Find in Files option that supports regex. Finding the right regex was not too hard:
(.*(\R)){5}
This will find all characters on the line (.*), the line ending (\R – because Notepad++ has PCRE support) and then find that combination 5 times ({5}).
I placed that regex in the Find what box in Notepad++ Find in Files dialog. I left Replace with blank and set the Filters to *.sql.
Here is how I set up the Find in Files in Notepad++ (version 7.1):

I had 697 files to process and Notepad++ did that in under 2 minutes.
Background
I had created SQL scripts from a database, but SSMS had helpfully added a descriptive line and then a few unwanted SET statements, like so:
/*** COMMENTS ***/ SET SOMETHING GO SET SOMETHING GO
Then, I also opted to have SSMS save the files in Unicode because, well, why not? Turns out the Windows command interpreter’s FOR /F doesn’t support UTF-8.
I could have regenerated the scripts, but I no longer had access to the source database server, so I had to deal with with I had available.
I hope this tip can help you, but I look forward to your comments on improving the solution!