Your situation
Seems you have two different versions of nodejs installed, possibly one was installed from sources and one from package manager like apt.
louis@louis:~$ node -v
v5.10.0
This returns older version of nodejs that you installed, I recommend you to remove it.
louis@louis:~$ nodejs -v
v6.2.1
This returns the current version of nodejs installed, possibly you installed it using package manager, I remember in Ubuntu it comes by nodejs executable name. 
I suggest you to create link like this 
sudo ln -s `which nodejs` /usr/bin/node
so it will be available using node command also.
nodejs vs node on ubuntu 12.04
louis@louis:~$ npm -v
3.8.3
This is just version of your npm program and has nothing to do with nodejs version.
Better solution
Uninstall all versions that you have and install node using nvm to switch between old/new versions easily
To install or update nvm, you can use the install script using cURL:
curl -o- https://raw.githubusercontent.com/creationix/nvm/v0.31.1/install.sh | bash
or Wget:
wget -qO- https://raw.githubusercontent.com/creationix/nvm/v0.31.1/install.sh | bash
Usage
To download, compile, and install the latest v5.0.x release of node,
  do this:
nvm install 5.0
And then in any new shell just use the installed version:
nvm use 5.0
https://github.com/creationix/nvm#install-script