PostgreSQL 9.5 is now available:

https://wiki.postgresql.org/wiki/What's_new_in_PostgreSQL_9.5

It has scalability and performance enhancements which should make it desirable to use with larger Bitbucket instances.

Please start the process for adding support for PostgreSQL 9.5 to Bitbucket Server.

I have it installed on a personal instance, and other than the red warning that Bitbucket Server puts on the top of the screen, I haven't noticed any failures or problems. I expect few changes to be required, and this is more a matter of the support and testing infrastructure requirements.