Ruby on Rails and Postgresql - Server is running, but I'm obtaining a could not connect to server error

QUESTION: PostgreSQL server is running, but when I run rake db:migrate, I obtain a ConnectionBad: could not connect to server error. What can I do to fix this error?

Update - Database.yml file

I've removed some points in the file for anonymity.

default: &default
  adapter: postgresql
  pool: 5
  timeout: 5000

development:
  adapter: postgresql
  encoding: unicode
  database: db_development
  pool: 5
  username: 
  password: 

test:
  adapter: postgresql
  encoding: unicode
  database: db_test
  pool: 5
  username: 
  password:

production:
  adapter: postgresql
  encoding: unicode
  database: db_production
  pool: 5
  username: 
  password:

I've looked through the API and tried to implement the answers, but nothing is working on my end.

When I run pg_lsclusters, I'm told:

Ver Cluster Port Status Owner    Data directory              Log file
10  main    5433 online postgres /var/lib/postgresql/10/main 
/var/log/postgresql/postgresql-10-main.log

So it's online, I usually start the server as sudo service postgresql start.

However, when I try and run rake db:migrate, I get the error:

PG::ConnectionBad: could not connect to server: No such file or directory Is the server running locally and accepting connections on Unix domain socket "/var/run/postgresql/.s.PGSQL.5432"?

I haven't encountered this error before, is it possible I have uninstalled postgresql wrongly?

I did it as: sudo apt-get update sudo apt-get install postgresql postgresql-contrib libpq-dev gem install pg

And in the Ruby on Rails app:

bundle install bundle update

Everything installed perfectly, so I just don't know what I have done wrong, given I've done those steps before on another computer and it works fine for it.