*NIX (Linux, OS X, ...)

Use n, an extremely simple Node version manager that can be installed via npm.

Say you want Node.js v0.10.x to build Atom.

npm install -g n   # Install n globally
n 0.10.33          # Install and use v0.10.33

Usage:
n                            # Output versions installed
n latest                     # Install or activate the latest node release
n stable                     # Install or activate the latest stable node release
n <version>                  # Install node <version>
n use <version> [args ...]   # Execute node <version> with [args ...]
n bin <version>              # Output bin path for <version>
n rm <version ...>           # Remove the given version(s)
n --latest                   # Output the latest node version available
n --stable                   # Output the latest stable node version available
n ls                         # Output the versions of node available

Windows

Use nvm-windows, it's like nvm but for Windows. Download and run the installer, then:

nvm install v0.10.33         # Install v0.10.33
nvm use v0.10.33             # Use v0.10.33

Usage:
nvm install [version]        # Download and install [version]
nvm uninstall [version]      # Uninstall [version]
nvm use [version]            # Switch to use [version]
nvm list                     # List installed versions

nvm install 8.10.0 is for installing proposed node version locally.

In order to use it:

nvm use 8.10.0

Note that you need to run this command as administrator.

You can always set default Node.js version:

nvm alias default 8.10.0

As noted in another answer, there is now a command for this:

nvm now has a command to update npm. It's nvm install-latest-npm or nvm install --latest-npm.

nvm install-latest-npm: Attempt to upgrade to the latest working npm on the current Node.js version.

nvm install --latest-npm: After installing, attempt to upgrade to the latest working npm on the given Node.js version.

Below are previous revisions of the correct answer to this question.

For later versions of npm it is much simpler now. Just update the version that nvm installed, which lives in ~/.nvm/versions/node/[your-version]/lib/node_modules/npm.

I installed Node.js 4.2.2, which comes with npm 2.14.7, but I want to use npm 3. So I did:

cd ~/.nvm/versions/node/v4.2.2/lib
npm install npm

Easy!

And yes, this should work for any module, not just npm, that you want to be "global" for a specific version of node.

In a newer version, npm -g is smart and installs modules into the path above instead of the system global path.

This may work:

nvm install NEW_VERSION --reinstall-packages-from=OLD_VERSION

For example:

nvm install 6.7 --reinstall-packages-from=6.4

then, if you want, you can delete your previous version with:

nvm uninstall OLD_VERSION

Where, in your case, NEW_VERSION = 5.4 OLD_VERSION = 5.0

Alternatively, try:

nvm install node --reinstall-packages-from=current

Or you can update to the last long-term support version with

nvm install lts --reinstall-packages-from=current

You can set the system-wide Node.js version by typing

nvm alias default 11.10.0

Install the version that you would like:

nvm install 11.10.0

Set 11.10.0 (or another version) as default:

nvm alias default 6.1.0

Verify the current version by running node -v or nvm current