So whatever chord progression is going on I can play any scale over it as long as they have the same notes as the chord progression? For example, say I have E5 F5 A5 as rhythm as long as the scale has E F A in it I can play/solo over this?
You should take into account the other notes of the chords

E5 is E and B
F5 is F and C
A5 is A and E

So all the notes in the chords are A B C E F
Choose any scale with these notes to play with (note that you're pretty much limited to C major/A minor)
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Yes you want to take the other chord notes into account not just the root as Prime has mentioned.

It also depends on your tonic. Which chord is the progression resolving to?

E5 F5 A5 don't appear to use C as the tonic since there is no C chord it can't resolve there. So you wouldn't be using C major scale so A minor may work in this case.

I fear going here but...depending on your arrangement of the chords you could if you're resolving to E use E Phrygian or if your progression resolves to F use F Lydian.