... For a five piece kit, start out on the highest tom, work down the toms, and finish with the kick.
Just throwing this out there-- when I tune, I usually actually start with the bass drum, then go to the lowest tom, and work my way up. This is partly because I play rock and tune the bass and toms fairly low, and also because I find it easier to have to tune a drum up if it's too low, rather than have to tune a drum lower if it the pitch is too high relative to the rest of the drums. Not to knock you for what you do, just sharing my technique. If starting at the top and moving down from there works for you, then more power to you.
There are a couple of problems I see with the thread starter's original idea, which has been discussed a lot already. First of all, although it's already been said, it's totally impractical to try tuning your drums before every song to match the key of the song. Also, who's to say that you can match every
single note that the other members of the band play/sing? What if the song has a key change? What if the song has a million different chords? You can't be expected to match pitch with the other members of the band because the typical drumset isn't designed to do that.
I don't have a lot of experience with this so I could be wrong, but when I'm listening to music, my mind hears the harmonic structure of the song, that is, the chords and melody and everything, from the instruments that are meant to do provide it-- guitars, bass guitar, piano, singing (as far as rock music goes). In my experience, the drums don't "contribute" to the harmonic structure. If there ever was a song that I've listened to where (just for an example) the guitarist played a G major chord and the drummer played a tom at the same time that was tuned to a non-chord tone (let's say, a C natural), then it's never bothered me. Out of all the music I've listened to, there's got to be a large number of such incidences, but I've never been listening to music and suddenly think, "Wow! That drum is really dissonant when played with the other instruments in that part of the song." Maybe it's because-- though I do believe that toms will carry a definite pitch (sometimes with some degree of downwards pitch bend)-- the sound is so staccato and such a different timbre that the fundamental pitch gets lost to the listener? I couldn't tell you because I've never studied the idea that much in-depth.
All that being said, I will typically try to tune a perfect 4th or perfect 5th between my kit's 12" and 14" toms. I do believe that when you play a pattern between several toms, it's nice to hear exact intervals between them. It'd be an interesting experiment, maybe, to have a drummer tune three toms to form a diminished chord, or even a chord out of equal temperament (having some drums be 50 cents flat or something), then play a pattern that incorporates all three drums, and see if anyone would actually notice...