Oops...the 405 error was something else. So maybe I have 2 issues.
Sorry - I'm drowning in raw logs. The 405 doesn't give ANY further information. Just this:
[Thu Oct 31 16:57:32 2013] [error] [client 126.96.36.199] File does not exist: /home/myusername/public_html/405.shtml
[Thu Oct 31 16:57:28 2013] [error] [client 188.8.131.52] File does not exist: /home/myusername/public_html/405.shtml
I blocked the IP with the 405 error and also blocked "Mangoway" as a user agent in my .htaccess file. I hope that works because there are a gazillion IP addresses being used - not a normal browser string. Very strange that something redirects to my site to a page not found about 3 times per minute. ?