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If I play a pentatonic minor scale a fifth above the root, it sounds really good. Why?
As an example, if the band is playing a vamp on A major, I can solo on an E minor pentatonic scale for days.
Is there a theoretical reason for this or is it just a happy accident?
There are different ways to see it. Your E minor pentatonic fits there, because the notes of the E minor pentatonic added to an A major chord either support the A major, or add to it creating more complex chords. Additionally the G note does something that's not found in plain A major scale, making it a dominant chord (A7). When vamped over instead of resolving (to e.g. a D chord), you can think of a dominant chord as sounding bluesy or jazzy.
Let's see which chord is created as a result of adding each of the notes of the E minor pentatonic scale:
Or if you think that you're playing all of the notes at the same time, arpeggiating a chord, or actually playing them as a chord, and leaving out the notes that are already in A major (E and B), you create - A major + G + B + D = A11. An A11 chord is: A, C#, E, G, B, D.
... and G+B+D is G major - so depending on how you play the notes, you might be making it sound a bit like the chords A major and G major are alternating. The combined notes from A major and E minor pentatonic (A, B, C#, D, E, G) are the same as a combination of A major and G major triads.
Or you can think that you're (almost) creating the sound of the A mixolydian mode, if the backing chords stay in A major all the time, keeping the tonic fixed to A. (The feeling of a tonic i.e. home note is required in modes) The A major chord has the notes: A, C#, E. Add the notes from E minor pentatonic, and you get A, B, C#, D, E, G. The only thing missing form A mixolydian is F#.
Why does it sound good? Maybe you like the sound of the A mixolydian mode or the A11 chord. Maybe you like being able to create a harmony that's a bit more interesting than plain vanilla pop songs, and you can do it without playing any wrong notes? Who knows. I tried it, and I got tired of playing E minor pentatonic on an A major vamp after about two minutes. :) ... edit: it became more interesting again after awhile, when I forced myself to just keep playing and find different things to do with the notes. ;)
Perhaps you like the sound of the 9th. Why wouldn't you? The scale has the root, the fifth and the seventh, and then you add the ninth. Leaving out the third probably has a big effect---it doesn't tie you down to a particular sound (major or minor). It's more rock than blues.
The answers so far provide a lot of good info. Have you tried any other mixtures of modes or degrees? Like D min penta on A, or E Phrygian, E Major? The reason I ask is that there are "compatible keys" in western music theory and no surprise they fall on the circle of 5ths (or 4ths depending on which direction you go). You can see this from the tetrachords that make up the major scale. (Do, Re, Mi, Fa) has the same structure as (Sol, La, Ti, Do). For any key you are in there is a compatible key a 5th above you and one below you. For example in the key of C, the keys of G and F are compatible. They differ by only one note from the original key, very important notes to be sure but they are almost identical. It is common to modulate key to one that is in this group and to use these groupings and some other devices to walk to other keys that are not compatible. The transition from C to F (or G) is easy on the ear and one can play around with these transitions without sacrificing musicality. If you were to play the G major scale over C in the key of C this would be the same thing as raising the 4th of the Key of C. The 4th is typically viewed as an avoid note (especially in Jazz) and the raised 4th essentially means you are playing C Lydian. Many Jazz musicians default to Lydian on the 1 for solo ideas. They like that augmented 4th. I think you are experiencing a similar idea with playing E min pent over an A vamp. E and A are compatible. It might fun to explore other modes in this way.
Another point relevant to answering your question is that a one chord vamp doesn't really force one into a particular key. This can be a great opportunity to explore more than the blues. On tunes like this you can basically solo in any key that has A as a chord in the key (at least as a starter). But in fact you can solo "out of key". The Minor pentatonic and blues scale work over major chords even though they have a minor 3rd (I'm referring to A min pent over A maj or A7). In my opinion this is a cultural trait of "The Blues" and the thing that makes it sound so cool. You are adding the b3 (or #2 if you want to think of it that way) over the 3 and this creates dissonance, a sad feeling that is "blue". The b5 does the same. As others have said you are almost in A mixolydian and that works well over A. I would say that you are in several possible keys at once and you could toggle back and forth with many musical ideas in this case.
It's the same idea as a lot of beginner players use for a 12 bar 'blues'. If they know the pentatonic minor scale notes in, say, A, then they'll play those over all three chords in a 12 bar in A. That includes over the other two chords - D and E. So particularly over the D chord, it's exactly what you do. But it works (by and large) over all three.
There are always going to be a couple of 'avoid' notes when doing this, and in your case, the D note although it doesn't have to be avoided, is best used on a non-emphasised part of a bar - your ears will often make that happen.
As piiperi has explained, it works because it adds extra notes which happen to fit well with the chord. The Am pent. notes are A C D E G. Your Em pent. notes are E G A B D. So the common ones are A D E G. Leaving only the B instead of C. As a 9th (of A) it's going to fit well over A.
Let's take it a little further. That 12 bar in A. Add the notes from Dm pent. into the mix. D F G A C. Again, plenty of common notes - D G A in all of them! No wonder just using Am pent. fits (nearly) all! The only note standing on its own here is F. So an 'avoid note' for A and E bars. But, lots of players still use it, anywhere they like in a 12 bar. In fact, I go as far as to tell students that any note can be made to fit anywhere in any chord sequence - providing they put it in musically, and that fact gets proved over and over in many great pieces. And I'm not just considering jazz here!
Lots of good answers here. For those who are visually inclined, here's an example of why the minor 5th pentatonic sounds so good, especially over a mixolydian scale.
Source: https://www.guitarscientist.com/generator/index.php?frb=227yeUThPvNDTt4
(I'm not affiliated with Guitar Scientist in any way, I just like to use them to draw fretboard diagrams.)
It's not so much that a pentatonic sounds good, more that it doesn't sound bad! Self-taught pianists often play 'on the black keys' in Gb major, because mistakenly-hit 6ths and 9ths are a lot better than 7ths and 4ths.
You can noodle inoffensively on a pentatonic. It doesn't have as many wrong notes!
