If you want to play, let's say A major chord, you can play it on various positions on guitar, as long as you have A, E and C# notes in it.

Why should we play the same chords in different way?

Because:

1. - We get a bit different tone,
2. - We get new positions and therefore new options to play certain chord progression which makes it easier for us once we overcome barre chords
3. - It is much easier to coordinate with barre chords (in the beginning) when dealing with chord progressions than with open chords only
4. - We can.

How to play that A major chord, starting from 5th fret of low E string?

First, you put your index finger over all strings on 5th fret (this is what barre chords are named after, because you 'barre' all strings on one fret). Maybe you will be able to do this from first try, and maybe you'll have to work on this. Don't get discouraged if you won't be able to execute this immediately. It's hard for beginners, and it takes practice and time to overcome it. If you won't be able to do it only with index finger, put the middle finger on it so you get more pressure strenght. That's a good practice. But you should be able to do it with index finger only to get barre chords right.

Then, put ring finger on 7th fret of 5th string, and then your pinky on 7th fret of 4th string. Then put the remaining middle finger on 6th fret of 3rd string. You should get this:

Strum each string to hear if it rings clearly. It often occurs that beginners have a problem with getting a proper tone while pressing the strings with lower part of their index finger. That is totally normal. Don't think you're not 'destined' to play barre chords or something. You'll get it over time. 

Ok, that's A major chord, now where are all the others?

That's how it looks for major barre chords on all 6 strings. You basically take the fingering of open E chord, where you put pinky and ring finger on 2nd frets, and middle finger on 1st fret. Then you just barre the string before them as you move them up the neck. And relative to that keys change, too. 

Here's the chart for minor chords in the same position;

Those are even easier to play than major ones. 

You can also play barre chords on 5 strings only. Let's begin with minor chords, because (what an irony), they have almost same fingering as major chords have on 6 strings;

And of course, major barre chords. They have a slightly different fingering now. If you're about to play A# major barre chord, you should put middle finger, ring finger and pinky on 3rd fret, and barre 1st fret with index finger. Alternatively, you could barre 1st fret with index finger and also barre 3rd fret with ring finger. Although, I heard that's not healthy for ring finger, because it's being bent unnaturally (I do it like that in most cases, anyway).

That's it for now about barre chords. You're on your own now. Practice those out. Once you've got them in under your belt, learn to play all the songs you know without open chords. Use only barre chords. That's one pretty good exercise.

Keep on rockin'!