You can update WordPress to its latest version through FTP.

Warning: You should always backup your site before updating.

Deactivate all of your plugins.

From the Dashboard menu, click Updates.

Under the heading "An updated version of WordPress is available," click Download to get a .zip file containing the new version of WordPress. The file will be downloaded to your local computer.

Note: Alternatively you can download the .zip from the WordPress Release Archive.

Unzip the file.

Note: If you don't have a way to unzip the file on your hosting account, you'll need to unzip the file on your local computer, and then upload the unzipped folder of files.

Connect to your hosting with FTP.

Delete the /wp-admin and /wp-includes folders.

Delete all files in your WordPress site's home directory, except the .htaccess, wp-config.php and robots.txt files.

Upload the files, wp-content folder, and wp-includes folder from the unzipped WordPress folder on your local computer. You can skip the wp-content folder for now.

When prompted, click Update WordPress Database.

Once complete, click Continue

If you have any default WordPress themes installed you can now update them from within the WordPress dashboard.

You can now activate your plugins again.