Yeah, it is running on WP 3.5.1.
I think I can do the manual upgrade from 3.5 to 3.5.1
But these notes bugs and scares me:
NOTE - you should replace all the old WordPress files with the new ones in the wp-includes and wp-admin directories and sub-directories, and in the root directory (such as index.php, wp-login.php and so on). Don't worry - your wp-config.php will be safe.
Does this note defines no. 4 and 5 instructions?:
3. Delete the old wp-includes and wp-admin directories on your web host (through your FTP or shell access).
4. Using FTP or your shell access, upload the new wp-includes and wp-admin directories to your web host, overwriting old files.
Be careful when you come to copying the wp-content directory. You should make sure that you only copy the files from inside this directory, rather than replacing your entire wp-content directory. This is where your themes and plugins live, so you will want to keep them. If you have customized the default or classic themes without renaming them, make sure not to overwrite those files, otherwise you will lose your changes. (Though you might want to compare them for new features or fixes..)
I got plugins, themes and index on wp-content. I'v downloaded the WP 3.5.1 from http://gadjade.com/wp-admin/update-core.php. Is this the one that is right?