I was very surprised reading through all the comments and not one person mentioned the biggest and most important reason for working with the latest versions of most any software language....SECURITY.....
Do not deploy with PHP versions 3 or 4. There are far too many security issues and they no longer have support in the PHP community. You will also limit yourself in what you can accomplish with those two older languages.
I have included a high level overview of some of the major changes that occurred in the development of PHP. This is by no way a complete list as that would take days to put together, there have been 10's of thousands of changes to the language just over the last five or six years.
PHP3 - (No Longer Supported) Oct. 2000, was a good server side language that gave us web developers an opportunity to work with the server side of our applications, this was one of the first languages available to web developers that allowed this, at that time the web was very new and static web pages were the norm. Originally develop as a Personal Home Page language, Rasmus Lerdorf in 1994, he developed the language for his personal use, it worked but had many areas that needed to be developed. There was only one version of PHP3 it was quickly replaced by PHP4 in just a few short months.
PHP4 - (No Longer Supported) developed and released in May 2001 was a vast improvement to PHP3. Initial types of security was implemented and support of Arrays was added this was a large step forward. Version 4 went through many updates over the years and major upgrades to the language were occurring approximately every 3 months, the PHP group began to grow and the development was very instrumental in the changes that were occurring and the implementation of database support. As popularity grew there were still many issues discovered with the security implementation of the langauge across larger sites. Version 4 was the first version that supported the Apache server configuration, as that was becoming the most popular web server being deployed. Many security issues and numerous language updates occurred throughout the life-cycle of PHP4. The first real SQL middle-ware was developed during version 4 and full support for remote databases was established.
PHP5 - released in July 2004 this was a major upgrade to PHP. Still under active support. Supported much better error handling, completely rewritten UNIX and Windows handlers, for better speed and security updates. Support for XML files was added in a early version of PHP5 and became very popular as data structure format. Support for SSL was added. Meta tag support was added as SEO became much more important as the web began to grow. Major security issues were addressed with additional support for hashing and the beginnings of the SALT functionality was being added to the language. Throughout the course of the Version 5 development thousands of bugs were addressed and fixed, security were constantly being identified and addressed and speed and 64 bit support were addressed and added. Extensions were added to the language to allow for connections to multiple database architectures and MySQL soon became the most popular database for the web. This still holds true even today although there are new database architectures that are catching up. MD5 encryption scheme was developed and added to PHP5. The popularity of OOP started to drive the development of PHP in a more class based language. As their popularity increased support for JavaScript, jQuery and JSON were added to the language. Version 5 eventually split into 2 separate branches of development, one branch staying in the procedural mode of development and the other working towards a class branch development. The last major update to PHP Version 5 occurred in July of 2017. There are well over 100 versions of PHP5 addressing enhancement to the language and fixing bugs that have been identified.
PHP6 - never officially released and development scrapped in June 2014.
PHP7 - Released Dec. 2015. Speed and multi-thread asynchronous support was the major driving factor. Numerous security updates and encryption updates added to the initial release. Growing in popularity but still way behind PHP5 in deployments.
I hope this helps.