How to get npm 5.6.0 while running ubuntu:16.04 container

My configuration:
Ubuntu 16.04
npm: 5.6.0
node: 8.0.0

I entered the command lines:
docker pull ubuntu:16.04
docker run -it ubuntu:16.04
then, as a root:

apt-get update
apt-get instal npm

and after the installation succeeded,

npm install npm@latest

The problem is that, when I enter, while running ubuntu:16:04 container,
npm -v

I only have the version 3.5.2
How can I upgrade the npm and node versions inside the image?

I need more recent versions (I would like to get the npm 5.6.0 version) in order to be able to build another project inside the ubuntu image.
Thanks in advance!