They are called "5 note chords" and "6 note chords" because they are not so fundamental a component of music that they need a shorter name.
A "triad" applies to many different three-note chords - always based around the root, a third, and a fifth -- but the third may be major (4 semitones from the root) or minor (3 semitones from the root), and the fifth may be perfect (7 semitones from the root) augmented (8) diminished (6).
You've encountered a four-note dominant 7th chord, which is a major or minor triad plus a flattened 7th. But there are lots more 4-note chords - any combination of four notes, some more pleasant sounding than others.
The article you've linked has helpfully colour-coded the notes in the chords. Let's look at one of the chords - the second chord in this piano roll:

The author has already told you the colour coding: root (purple), 3rd (blue), 5th (yellow) and 7th (green).
This 6 note chord contains:
- Ab (root)
- C (3rd)
- Eb (5th)
- G (major 7th)
- C (3rd)
- Eb (5th)
Note that there are two 3rds and two 5ths. This is a 4-note chord, an Ab major 7th, with two of the notes doubled up by playing their octaves.
The author also tells you:
Notes highlighted in red aren’t in the basic chords, but are added on top to form a simple melody
The following "8 note" chord is really a four-note chord -- C minor 7th -- with two notes doubled up, to make it 6 notes, and two melody notes, which are not part of the chord as such.