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Installing nginx is straightforward, so I will not go into details, just check the nginx documentation for more.

First create a repo file.

vi /etc/yum.repos.d/nginx.repo

and add following content to repo file:

CentOS
[nginx]
name=nginx repo
baseurl=http://nginx.org/packages/centos/$releasever/$basearch/
gpgcheck=0
enabled=1

To install php 5.3.8 we need extra repos (source article).

## Remi Dependency on CentOS 5 and Red Hat (RHEL) 5 ##
rpm -Uvh http://download.fedora.redhat.com/pub/epel/5/i386/epel-release-5-4.noarch.rpm
 

## CentOS 5 and Red Hat (RHEL) 5 ## 
rpm -Uvh http://rpms.famillecollet.com/enterprise/remi-release-5.rpm

Install using added repos.

yum --enablerepo=remi install nginx php php-fpm php-common

Install necessary php modules for you.

yum --enablerepo=remi install php-pear

Start Nginx

/etc/init.d/nginx start ## use restart after update
## OR ##
service nginx start ## use restart after update

Start PHP-FPM

/etc/init.d/php-fpm start ## use restart after update
## OR ##
service php-fpm start ## use restart after update

Autostart Nginx on boot

chkconfig --add nginx
chkconfig --levels 235 nginx on
#Autostart PHP-FPM on boot
chkconfig --add php-fpm
chkconfig --levels 235 php-fpm on

Now it is time to configure nginx to work with php.

vi /etc/nginx/conf.d/test.conf

put these lines into file.

server {
    server_name example.net;
    access_log /var/logs/nginx/example.access.log;
    error_log /var/logs/nginx/example.error.log;
    root /var/www/example;
 
    location / {
        index index.html index.htm index.php;
    }
 
    location ~ \.php$ {
        include /etc/nginx/fastcgi_params;
        fastcgi_pass  127.0.0.1:9000;
        fastcgi_index index.php;
        fastcgi_param SCRIPT_FILENAME /var/www/example$fastcgi_script_name;
    }
}

restart nginx

service nginx restart

create an index file to test.

vi /var/www/example/index.php

<?php phpinfo(); ?>

Mercurial may not be present in default repo that comes with a fresh Centos 5 install. Adding RPMForge repo should solve the problem. I will copy paste necessary section from Centos wiki:

Download the rpmforge-release package. Choose one of the two links below, selecting to match your host's architecture. If you are unsure of which one to use you can check your architecture with the command uname -i

for i386 :

wget http://packages.sw.be/rpmforge-release/rpmforge-release-0.5.2-2.el5.rf.i386.rpm

for x86_64:

wget http://packages.sw.be/rpmforge-release/rpmforge-release-0.5.2-2.el5.rf.x86_64.rpm

The preferred rpmforge-release package to retrieve and to install in order to enable that repository is one of the two listed above.

Install DAG's GPG key

rpm --import http://apt.sw.be/RPM-GPG-KEY.dag.txt

Verify the package you have downloaded

rpm -K rpmforge-release-0.5.2-2.el5.rf.*.rpm

Security warning: The rpmforge-release package imports GPG keys into your RPM database. As long as you have verified the md5sum of the key injection package, and trust Dag, et al., then it should be as safe as your trust of them extends.

Install the package

rpm -i rpmforge-release-0.5.2-2.el5.rf.*.rpm

This will add a yum repository config file and import the appropriate GPG keys.
Then try to install something like this

yum install mercurial

it is done.