8-10-10 E root is a C5 chord. 3-5-5 A root is a C5 chord. This is why you need to know the notes on atleast the E and A strings.
Every 5th frets on the E A D G is the same pitch as the next string.
E-5 is an A E-10 is a D E-15 is a G. So when you power/barre chord reaches the 5th fret yiu can play it on the next string 5 frets lower.