Hi,
you a 'little bit' late. :-)
5.5.12 is the latest release under the old LTSR schema. 5.6 is under support a year longer than 5.5.12. There is no EOS for 5.7 given, but simple logic says it must be at least a year after 5.6.
We do have a few 5.5.8 customers that we advised to go to 5.6 and will now advise to go to 5.7.
IBM does a pretty fantastic job in avoiding regression problems so we go much more confidently into such upgrades as 10 or 15 years ago.
Kind regards,
/Gerold