Are new licenses for CLM 6.0.x also compatible with CLM 5.x?

I don't think there is any statement about this. In general there is an N-1 compatibility (see https://rsjazz.wordpress.com/2013/07/09/new-version-and-now-experiences-with-sdk-and-plain-java-api-across-tool-versions/ ) and while upgrading you will have to be able to work in a mixed version, which would suggest that the new licenses on the 6.x JTS should work with the 5.x applications. I tested some licenses and it worked for this combination. I am however not aware of any statement that this is guaranteed.