Peer authentication failed for user with all privileges in Postgres 9.5

Open /etc/postgresql/9.5/main/pg_hba.conf with root access

 sudo nano /etc/postgresql/9.5/main/pg_hba.conf

Change peer to md5 in these lines.

Before changing

# "local" is for Unix domain socket connections only
local   all             all                                     peer
# IPv4 local connections:
host    all             all             127.0.0.1/32            peer
# IPv6 local connections:
host    all             all             ::1/128                 peer

After your change

# "local" is for Unix domain socket connections only
local   all             all                                     md5
# IPv4 local connections:
host    all             all             127.0.0.1/32            md5
# IPv6 local connections:
host    all             all             ::1/128                 md5

Save the file with pressing Ctrl-O. Exit nano with Ctrl-X

Restart postgresql using

sudo service postgresql restart