The 4.x is the version that is currently being supported, similar to a production release. The 5.0 version is stable, but it is the upcoming version in flux and should be treated like it is a beta or release candidate. As such you currently do not see 5.0 as an option in things like Amazon Elastic Beanstalk.
Once a Stable release line becomes LTS, no new features or breaking
changes will be added to that release.
To understand the difference you need to understand why a Long Term Support (LTS) version of Node exists.
Node LTS is primarily aimed at enterprise use where there may be more resistance to frequent updates, extensive procurement procedures and lengthy test and quality requirements.
From Rod Vagg a member of the Node LTS working group:
The point of establishing an LTS plan for Node is to build on top of an existing stable release cycle by delivering new new versions on a predictable schedule that have a clearly defined extended support lifecycle. While this may seem at odds with the open source tradition of “release early, release often” it is an essential requirement for enterprise application development and operations teams. It also affects companies ... that provide professional support for Node.js.
It is sometimes misunderstood that odd version number releases (v5, v7) are a "beta" of the next LTS release. This is a convention used in other project but not in Node and is somewhat misleading. In fact, the next LTS release is chosen from a specific point release of the current version, and this will usually be an even version release (v6, v8). It's not that the latest versions are betas - it's that the LTS releases fulfil a specific need some organisations have.
Generally if you are able to keep up with the latest stable and future Node releases you should do so. These are stable and production ready releases with excellent community support. Unstable and experimental functionality is kept behind build and runtime flags and should not affect your day to day operations.
Generally I always lean towards the latest version for features and performance (as I now do allot of ES6 / ES7)
This would suggest to me that stable versions and beyond will suit your needs well. This will give you access to the latest and greatest language features provide by the underlying JavaScript engine (V8 or Chakra)
Of note: A significant difference between v4 (and earlier) and v5 is that v4 ships with npm v2 whereas v5 ships with npm v3. v3 of npm has some potentially breaking changes for your project in how it handles peerDependancies. The way npm v3 now tries to install a dependancies own dependancies as flat as possible and avoid duplicates may affect your projects but has been a big boon for Windows users so this may also impact your decision making.
Current: Under active development. Code for the Current release is in the
branch for its major version number (for example,
v10.x). Node.js releases a new
major version every 6 months, allowing for breaking changes. This happens in
April and October every year. Releases appearing each October have a support
life of 8 months. Releases appearing each April convert to LTS (see below)
each October.
LTS: Releases that receive Long-term Support, with a focus on stability
and security. Every even-numbered major version will become an LTS release.
LTS releases receive 18 months of Active LTS support and a further 12 months
of Maintenance. LTS release lines have alphabetically-ordered codenames,
beginning with v4 Argon. There are no breaking changes or feature additions,
except in some special circumstances.