Is there any way to install MySQL 5.1 and PHP 5.3 on Centos 7. I researched a lot but could not find any link which gives step by step procedure. Can someone please give me steps to be followed to install these .
There are no RPMs of MySQL 5.1 for CentOS 7. Your only chance is to take the "generic tar-ball", its installation is described in the manual. At the top of my head, I see two potential points of trouble:
1) You may need to disable SElinux.
2) Some system library may have had an API change between the build platform of the binaries and CentOS 7.
I have no info on PHP.
Try using IUS Community Project repositories:
yum -y update yum -y install epel-release wget https://centos7.iuscommunity.org/ius-release.rpm rpm -Uvh ius-release*.rpm yum -y update yum -y install php56u php56u-opcache php56u-xml php56u-mcrypt php56u-gd php56u-devel php56u-mysql php56u-intl php56u-mbstring php56u-bcmath
You can change php5X or 7x for versions you want.
Another way to run ANY PHP version over any linux distribution is compiling it from sources. Its simple. Look this manual that explain how to run any version of PHP: https://docs.google.com/document/d/1WSJ0LMIJW5syLCekyYTZALe4X_t_RI9umKwpM_2sO7g/preview