A is actually the 6th note in the C Major scale...this means that it is already a mode of C...So, really you're still in the key of C, but you're playing at one of the most known modes, which has become a key in its own right..The important thing is you realise the A Minor is the relative minor if C Major (Ionian), or that it is the 6th note is the C Major scale...So, by playing the 5th mode of A minor, you're really playing the 3rd mode of C Major...
Major Key 1 2 3 4 5 6 7
Note C D E F G A B
Am Note 3 4 5 6 7 1 2
Major Key 6 7 1 2 3 4 5
Note A B C D E F G
Am Note 1 2 3 4 5 6 7
So it's the same scales, same key, different starting note...
Hopefully I've helped you out here, if not, ignore me and I'll try again...I was in a bit of hurry...Good luck and take your time, it'll all make sense eventually...
Don't worry too much about me, ignore me long enough and I'll go away.