Great question!
Sorry about the late reply. In short, it is fine for the chord to be 1,5,1,3,5. As long as it has 1, 3 and 5, all is well.
If you were playing piano, where all the notes are laid out in nice rows, you would play 1-3-5 in a row. But with the guitar, often you can't easily play the notes in that order. If you think about where the C is in the A major chord, it is on the 3rd fret of the A string. But you are already playing the A string for A, and can't play both notes on one string.
Have fun,
Jon