To be able to play these types of chords in songs you have to know how to tune your guitar.
The standard tuning on a guitar from thin to thick strings is E B G D A & E. When you play a song using drop D tuning you tune the 6th string (thickest) from an E note down to a D (2 frets).
When you tune normally you use the 5th fret and open string below method as shown in the tuning section . To tune your 6th thick string down to a "D" note you have to play the note on the 7th fret 6th string and compare it to the 5th string open underneath it. Remember, you tune the 6th string 7th fret down to the same sound as the 5th string open.
Placing Drop D 5th Chords
Placing or naming drop D 5th chords will be the same way you name bar chords or normal 5th chords, you will use the 6th string as the root note. Unlike bar or 5th chords you will only use the 6th string as the root note. You can not transfer the shape down to the 5th string and play a root 5 position. There is no commonly used root 5 or 4 drop 5th chords.
Drop D 5th Chords
Since the 4th string is also a D string, you can include it with this chord, the choice is yours. When you include the 4th string it makes the chord full and rich, with a distorted amp it sounds great.
There is also a lot of songs that use Drop D for main song riffs, Some of these bands are Rage Against The Machine, Metallica, Silverchair, Lifehouse, Limp Bizkit & Korn (although some of these bands have seven string guitar and the seventh string goes down to a low B note).