Ok...you got 3 frets that give practical harmonics for tuning. Harmonics plucked above the 5th give the same note of each respective open string, only several octaves higher. 12th fret ones are a few octaves below the 5th's, but again the same notes. The 7th fret harmonics yield the same notes as the 7th fret notes if you were pushing down.
Here's how it looks:
5th fret: EADGBE 12th fret: EADGBE
7th fret: BEADF#B

So hit the harmonic on the 6th string, 5th fret...and while ringing, hit the one of the 5th string, 7th fret. All strings will tune this way (5th fret harm = 7th fret harm of string below)...except the 3rd string (G) trying to tune the 2nd string (B). Yet looking above you can see 2 different octaves of B harm availble on either E string at the 7th fret. That's the basic jist of it.
Use this in addition to open strings, chords, and/or the method you already use. Tuning is never perfect. You just have to kinda find the best average compromise. Does that make sense?