Please move this thread into the https://central.owncloud.org/c/help/miscellaneous category as is not an issue of ownCloud itself but of your webservers configuration.
405 means “Method not allowed”. Something in your webserver config or some other security module is blocking the WebDAV calls used by the client. There is a FAQ available here providing all known info about such webserver configuration issues: How to fix CalDAV|CardDAV|WebDAV problems
Once the search is working again you might also want to use the search of the forums for the keyword “method not allowed”.