Public key for is not installed

The .rpm package has been signed with a private key to provide nonrepudiation and integrity, basically, its genuinety. The package should be verified with the public key.

You can use rpm to install the package:

# rpm --import http://mirror.centos.org/centos/RPM-GPG-KEY-CentOS-5

# yum install ./mysqlclient10-3.23.58-9.2.c4.x86_64.rpm