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First of all, they're not even chords, they are intervals. But power chords (especially the 5th) have been responsible for much mayhem in musical history. During Bach's time there was a rule against using the 5th interval too much in a composition because it was considered to be "evil". With the onslaught of Rock 'n Roll the 5th interval has dominated the entire genre. In this sense, I guess the older generation was right when they said we were "going to hell" for listening to Rock music.
In fact, the 5th interval has so dominated Rock 'n Roll that you could play a multitude of songs using it and nothing else. Many players have made a pretty good living from power chords, and no doubt, many will still. When you hit a power chord on an electric guitar with the volume and distortion up, it sounds like all hell has broken loose. And I'm gonna show you how to use it, heh, heh, heh.
If we take a major scale, let's say in the key of C:
C D E F G A B C
And use numbers instead of note names, so we have:
1 2 3 4 5 6 7 8(or 1)
We can use this numbering system to figure out things and it will be valid for any key, since all major scales have the same configuration or shape (that shape is what makes it a major scale). See my page on the Numbering System for a more in-depth explanation of this idea.
This part is too simple:
Go to the Ear Training page if you want to learn more about octaves.
Let's look at this on the guitar. Below we have a diagram of the major scale using the numbering system. Try this out in different spots on your guitar, playing from 1 to 8 (the higher 1) to see that it always comes out sounding like the "Do, Re, Mi..." thing. Keep this on the three lowest strings for now, just like the picture shows.

For now we are just concerned with the 4th and 5th intervals, so let's isolate those:
Take the 5th interval, for now, and get used to moving it around on the guitar. It's like a two finger chord. Real simple. Does it have a familiar sound? It should if you're into Hard Rock, Heavy Metal, Punk, or any of the new rough-edged stuff.
Let's try a tablature example of a power chord riff. The following lick is similar to something Nirvana did with power chords:

Get used to moving the 4th interval around for a while. It's much easier to get used to as it only takes one finger barred across two strings. Notice that the sound is kind of similar to the 5th.
Try the following example. It's the riff from "Smoke on the Water" by Deep Purple. It employs all 4ths until the final chord which is a 5th.

The 4th and 5th intervals sound so similar because they are opposite of each other, but with the same notes! What does that mean? Let me explain with a few diagrams. This time we'll use the actual note names instead of the interval numbers. We'll use the key of A and show a 4th and a 5th:
The A and D make a 4th and the A and E make a 5th. Now look at the following diagrams:
In the first diagram, we have a 5th in the key of D. It's a D with an A! The upside-down of a 4th in the key of A.
In the second diagram, we have a 4th in the key of E. It's an E with an A! The upside-down of the 5th in the key of A.
To put this another way, a 4th in the key of A is the same two notes as a 5th in the key of D. Going back to our numbering system, if you take the 1 and the 5 and flip them so that we use the 5 as the root, you now have a 4th (still using the same two notes).
Anyway, I hope that explains why the two intervals sound so similar. If not, just keep this idea in mind. Maybe it will sink in later. The most important thing is to get accustomed to the sound of power chords. If you do, you will start to hear them in all kinds of Rock tunes and this makes the job of figuring out those songs much easier.
Here's a link to a few freeware programs to help you in being able to recognize any of the intervals (or chords, or scales). I highly recommend using an ear training program daily. Over time it will make a huge difference in your musical ability.