PhpMyAdmin is third party package which is not updated by ‘yum’ or automatically. There are always some packages and software on server which needs to be manually updated. The reason behind this is to avoid compatibility issue (e.g. migration from MySQL 5.1 to 5.5) and system crashes.

What you need to do is rename old PhpMyAdmin folder, download new files to server from link (or upload from PC when doing via FTP) and then extract the zip in a folder with same name as last one. So, you can use SSH, file manager or even FTP.
Let us see the method using SSH.
Login to your server via command line. Then locate the old PMA folder and rename it,
e.g. From,
/var/www/html/phpmyadmin to /var/www/html/phpmyadminOLD
Use,
mv phpmyadmin phpmyadminOLD
Now create new folder at same location (here under html folder) with same privileges and properties,
mkdir phpmyadmin
Change prompt to newly created folder,
cd phpmyadmin
Now, pull the new phpmyadmin files from the source server,
wget http://kaz.dl.sourceforge.net/project/phpmyadmin/phpMyAdmin/4.2.5/phpMyAdmin-4.2.5-english.zip
or you can try different language, formats and versions from here,
http://www.phpmyadmin.net/home_page/downloads.php
Now extract this package. Command will depend,
tar -xvf phpMyAdmin-4.2.5-english.zip
or
unzip phpMyAdmin-4.2.5-english.zip
If sub-directory is created then move all the files to phpmyadmin folder. If you made any config file in older version then you shall copy that file to new folder,
cp /var/www/html/phpmyadminOLD/config.inc.php /var/www/html/phpmyadmin/
Now, go to browser and try to access PMA in old way. Login screen should greet you! Check it by using your databases (search, edit etc.). If all working fine, then you can delete your old folder.
Troubleshooting:
1. If you encounter ‘phpMyAdmin Error 404 Page Not Found’, then refer this article.
2. Missing extensions or MySQL root login error – Fixing PhpMyAdmin starting problems.
3. If you successfully logged in but getting this – ‘Error in processing Request. Error code: 403. Error Text: Forbidden’. Then this is mostly ‘blowfish_secret’ request. You fix it as shown here.
As always, any other issues and comments are welcome.