The great thing about the guitar is that all of our shapes - from scales to chords, are modular. This means that we can take the same shape, change its' location on the guitar, and get the same kind of sound in a different key.
What you may be doing is taking the minor pentatonic shape at the fifth fret and moving it down to the third fret. While this is still a pentatonic scale, it is no longer in the key of A - it is in the key of G. The pentatonic scale has only five separate intervals - the root note, a minor third, perfect fourth, perfect fifth, and minor seventh.
Theoretically speaking, if you start on an A, this will give you the notes A (root), C (minor third), D (perfect fourth), E (perfect fifth), and G (minor seventh). If you start on a G, all of the other notes move with it. So, you would end up with G (root), Bb (minor third), C (perfect fourth), D (perfect fifth), and F (minor seventh).
If you wanted to start on G but still play an A minor pentatonic scale, you would have to change the shape you are playing. Instead of using the 5 8 / 5 7 / 5 7 / 5 7 / 5 8 / 5 8 pattern (starting from low 6th string to high first string) on the third fret, you would have to use a different pattern - 3 5 / 3 5 / 2 5 / 2 5 / 3 5 / 3 5. If you are interested, I recommend you check out the five positions of the minor pentatonic scale - essentially, for every note of the scale we have, there are five different ways you can play it. Depending on where you start the scale, the shape can change.
I hope this helps!