Technically, a power chord isn't a chord at all. It's an interval. Chords are made up of three or more notes, whereas a power chord only has two.
The "first" and "fifth" denotes where that note lies in a given major scale. The simplest example is in C, where the scale is C D E F G A B. The power chord is the first and fifth notes in that scale, thus C (the lower sounding note, or root) and G (the higher sounding note.)
Other common examples would be in G major (G A B C D E F#) where the first is G and the fifth is D. E Major (E F# G# A B C# D#) would be E and B. F major (F G A Bb C D E) would be F and C.
Be careful not to mix scale degrees and chord intervals.
In a chord, the First (or Root) and the Fifth (an interval of a fifth above the Root), are distinct from the scale degrees.
In the Key of C, C is the first scale degree and G is the fifth scale degree but other chords in the scale can be played as power chords. For example, in the key of C, power chords could be played on:
C - (first scale degree) - power chord played as Root C and fifth interval G.
F - (fourth scale degree) - power chord played as Root F and fifth interval C.
G - (fifth scale degree) - power chord played as Root G and fifth interval D.
and so on...