The biggest change that users will see in Solr 5 from Solr 4 is that Solr is now deployed as its own server process. It is no longer a WAR file that is deployed into an existing Servlet container such as Tomcat or Jetty. The argument for this boiled down to "you don't deploy your MySQL database in a Servlet container; neither should you deploy your Search engine". By owning the network stack and deployment model, Solr can evolve faster; for example, there are patches for adding HTTP/2 support and pluggable authentication mechanisms being worked on. While internally Solr is still using Jetty, that should be considered an implementation detail. That said, if you really want a WAR file version, and you're familiar with Java and previous Solr releases, you can probably figure out how to build one.
As part of Solr 5 being it's own server process, it includes a set of scripts for starting, stopping, and managing Solr collections, as well as running as a service on Linux.
The next most obvious difference is that the distribution directory structure is different, particularly related to the old example
and new server
directory.