Just downloaded the latest solr-5.2.1.tgz release from here. According to this and this post, it should contain the warfile in the /dist subdirectory.
But I can't find the warfile in the distribution. Did this change in version 5.x? Where can I get a prebuilt warfile of solr-5.x to deploy on tomcat?
Since tomcat support seems to be disabled since 5.x I had to dig a bit deeper and finally I found docs how to start solr quite easily, even though its not on tomcat.
You just have to unpack the solr-5.2.1.tgz file and then go to /solr-5.2.1 and do
$ bin/solr start
which will start the solr server on default port 8983 permanently.
I actually considered deploying the warfile on tomcat the easiest way but that just comes with diverse logging errors you have to handle. So the described way was the one to go for me.