well, basically it's not that difficult but every installation is different.
A short summary is here:https://www.atomicorp.com/wiki/index.php/PHP
Bes thing to do in such cases is to have a test environment. I have one too.
And since you only have one server it's not like others having dozens or hundreds of different servers/configs.
I would suggest you the following.
Install VMWare Workstation(with costs) or VMWare Player (free) or SUN/Oracle VirtualBox (free)
After that you make a complete backup of your server via tar. similar to this:
tar -cvpf /backups/fullbackup.tar --directory=/ --exclude=proc --exclude=sys --exclude=dev/pts --exclude=backups
After that setup/install a vanilla virtual server the same you did with your rootserver
make a snapshot of it
and than restore/extract your backup.
Of course its not that easy.
When restoring into virtual server pay attention to the boot and harddisk related files and settings.
at the end it will pay out.
start with it and if you face problems just post exactly what you did and the error is.
When you test environment is setup you can try upgrading php on your testbox and see how everything is going.
ask question, get answers, test them and when everything is running in your testbox you can touch your livebox.