Broken after upgrade

I am left today, after an upgrade I think (Fedora 23 --> 24) with a
broken postgresql.

It used to work very well. The service is started with the systemd
unit file. I have now this error:

-----------------
postgres(at)thetradinghall ➤➤ systemd/system %
/usr/libexec/postgresql-ctl start -D /db/pgsql/data -s -w -t 270
FATAL: 22023: database files are incompatible with server
DETAIL: The data directory was initialized by PostgreSQL version 9.4,
which is not compatible with this version 9.5.3.
-----------------------

Googling it gave me some entries, but I couldn't find any clear
explanation and how to solve. It seems I need to initiate a new
database, but thereafter is not clear (how to use my old data and conf
files pg_hba and pg_ident).

Thank you for hints/links how to solve this issue.
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