I think it's one of those things that seems like a great idea in the rehearsal room, but doesn't really translate terribly well at concert volume - I've never seen a band that actually sounded great live, using Drop C.
Even Queens of the Stoneage : great band, great songs, great records - but live, the songs have the liveliness sucked out of them, with everything sounding veiled.
The amps, cabinets, and instruments, weren't really designed with that in mind - though I'm all for pushing the envelope, and abusing technology, so long as it sounds good.
I know this opinion isn't going to be popular ; but personally Drop D is as low as I'm happy going (and that's pushing it), because any lower than that, and it stops sounding like an electric bass.
At that point, there are any number of instruments (electric, electronic, woodwind, brass, hammered) that handle the really low frequencies much better, and with a much more interesting timbre.
That's why I won't touch a 5 string bass, when I can just reach for a synth / sampler.
One thing you could try, is tuning your bass down a whole tone, so that your D string becomes a C string.
But yes, you can just drop the E string down to C - though you ought to increase the gauge by 1 set per downward step, to retain tension, clarity, and intonation (which may require permanent adjustments to the nut).