Path in .bash_profile is not recognized
To add /Library/PostgreSQL/9.5/bin to the path simply add the line:

export PATH="/Library/PostgreSQL/9.5/bin:$PATH"


to the file ~/.bash_profile. If you have a second similar line starting with export PATH... try to concatenate them.

After adding then line quit and open Terminal.app or enter source ~/.bash_profile to reload the modified .bash_profile.

Check the path with echo $PATH (which should yield: /Library/PostgreSQL/9.5/bin:/usr/bin:/bin:/usr/sbin:/sbin:/usr/local/bin and the "existence" of psql with which psql: /Library/PostgreSQL/9.5/bin/psql.

Afterwards enter psql -d database_name -U database_user_name with the following result:

Password for user database_user_name: 
psql (9.5.1)
Type "help" for help.

postgres=# 


Simply entering psql is as futile as entering mkdir or ssh only.