Don't get hung up on the idea that a method name like "5th fret method" provides an adequate description of the method. I have never heard it called the 5th fret method myself, but of course that is one common way to tune by ear. There are many other ways to tune by ear, too.
Does the 5th Fret System Work?
Standard tuning for a guitar is E A D G B E. The notes are all a fourth apart, except for G and B which are a third apart. To tune by ear, you compare the note on the 5th fret of a string with the open string above it, unless you are comparing the G string with the B string, in which case you compare the note on the 4th fret of the G string with the open B string. This is a very common way of tuning by ear; of course you need to get at least one string in tune by other means, e.g., using a tuner, tuning fork, pitch pipe, or some other reference (say, another instrument you are playing with).
When you tune like this what you are really doing is finding the same note in the same octave in different places on the neck and comparing the two sounds. I often tune by comparing the notes at the 10th fret with the notes on the 5th fret. That is, D on the 10th fret of the sixth string and D on the 5th fret of the fifth string, etc., but F at the 10th fret of the third string compares with F at the 6th fret of the second string (because the sixth fret of the B string is an F in standard tuning). I do this because I spend a lot of time playing in the middle region of the neck, and this can help get things to sound the most in-tune in the places that I am usually playing.
Another method I sometimes use is to play across the neck: the harmonics at the 7th fret of the sixth and fifth strings, the fretted notes at the 9th fret of the fourth and third strings, the open B and high E strings. Here the harmonic on the sixth string, the fretted note on the 4th string, and the open B string are all B in the same octave, and should sound as the same pitch. The harmonic on the 5th string, the fretted note on the third string, and the open E string are all E in the same octave. With this method there are three points of comparison for two notes spread out over a part of the neck that gets used a lot. This can be a very useful comparison for tuning.
Pros and Cons
The standard tuning evolved over many years. There are other ways to tune. One of them is "all-fourths tuning" which makes the tuning symmetrical by removing the third between G and B. This tuning is E A D G C F.
This has what some consider an advantage in that scale and chord shapes do not change from lower string sets to higher string sets. Say you are playing a chord that uses only the 6th, 5th, 4th, and 3rd strings. If your guitar is tuned in all-fourths, you can just move the same shape to the 5-4-3-2 string set, or to the 4-3-2-1 string set without any changes to play the same chord (possibly with a different root). In standard tuning you would have to modify the first shape to play the same chord on 5-4-3-2, and then modify the shape again to play the same chord on 4-3-2-1.
There are also disadvantages to all-fourths. Barre chords become much more difficult to play. In Standard tuning when you barre across a fret with a single finger you get the fifth and root of the chord on top, with the top root doubling the bottom root on the low E string. In all-fourths you have to form a "crooked" barre to catch the notes of the top two strings one fret lower than the root on the low E string. Not impossible, but not for beginners. Another disadvantage of all-fourths, in my opinion, is that it reduces the variety of possibilities when chording. That is, in standard tuning some fingerings that are difficult or impossible to play on the lower strings become playable on a higher string set, and vice-versa. With all-fourths there is no variation in fingerings across the fretboard so an impossible fingering on one string set is an impossible fingering on all string sets. As I said before, this is an advantage for some, but can also be a disadvantage for others.
All of that said, there have been some notable players who use all-fourths tuning. Off the top of my head, I believe that Stanley Jordan and Tom Quayle both use or have used all-fourths.