I've been programming PHP since 4.3 was edge, shortly before the 5.x branch was introduced. PHP has done a good job of maintaining backwards compatibility, so much so that you can learn from a manual covering 5.3 and expect all the materials in it to work. Moving backwards is where there's a problem, but with time you'll get a handle on what was introduced with each version. In brief..
The oldest code you are likely to be asked to maintain will be PHP 4.x. The language's core is present here, but once you step into Object oriented programming this version will give you fits due to everything that's missing. If you run across a server running PHP 4.x the whole setup is badly out of date. You can't even get PHP 4.x packages precompiled for any distro anymore. If a project like this lands in your lap, the first priority should be migrating the code to a newer PHP, or scrapping it all and replacing.
Class scope was introduced, as well as much of the SPL (Standard PHP Library) which includes the spl_autoloader functions. The Reflection API also appears here I think, though the first few versions where buggy.
PDO became core. If you aren't using it, you should
Json_encode and Json_decode show up. There was at one time a major move to set PHP 5.2 as the compatibility floor for many PHP codebases and, until recently it has been the floor, with only some of the newer libraries like Yii2 setting the floor to PHP 5.4
Namespaces where added, along with closures.
Adds a new password library and generators
Improved the syntax for argument overloading on functions, functions can now be imported between namespaces.
As can be seen from the above, much of what is different about each version isn't stuff a beginning programmer is likely to make a lot of use of, with the exception of PHP 5.4's array syntax. So don't worry too much about which version as long as you are on the 5.x branch somewhere.