PHP MySQL library version 5.0.51a differs from your MySQL server version 5.1.61
There is a connection otherwise phpmyadmin wouldnt know what version the server is.

In most cases you can ignore that as only slight differences exist (for a full difference check the changelogs between the versions) 

apt-get install php5-mysql

yum install php5-mysql


one of those should update your php library and not show that warning