Of course there's the familiar BEADG and EADGC tunings, and I've seen some people use DEADG before so they don't have to detune for a drop D (basically using it as a 4-string otherwise). One that I've had fun with some times is DEADA or BDADA, which makes octave riffs dead simple (pardon the pun). Are there any other common/useful tunings for 5-string?
Depends what you want; for the real heavy stuff you could drop DEADG down a full tone to CDGCF.
Or you could tune it to a chord like E major perhaps [E B E G# B], or flatten the third(G#) to make it an E minor [E B E G B].
You can tune to pretty much any chord which takes your fancy; however bear in mind that tuning to a chord may restrict your options and lock you into a specific key signature;
When I started playing with a band that played in drop D I didn't want to give up the low growl of the B. So I tuned my 5 string from low to high BDADG. Don't know how common it is, but I really like it.
I do know the chapman stick tunes its 5 bass string in 5ths. So from low to high it would be CGDAE.
Five string double basses in symphony orchestras sometimes are tuned CEADG, with the idea that the lowest C corresponds to an octave below the celli's lowest note. However I beleive this is 'old school' and most players today use the BEADG tuning.
(Some four string symphony orchestra double basses has a 'drop-C' neck extension feature on the E string.)
(Some double bassists tune their four strings in fifths - CGDA - like the cello but one octave down. For instance jazz bassist Red Mitchell.)
Bass guitar soloist Michael Manring has used a range of alternate tunings for different pieces. On his Zon Hyperbass, he has a variable, calibratable "D-tuner" on each of the four tuning machines so he can raise or lower the pitch of each string by a specific amount quickly. There is a second tuning-lever system at the bridge for lowering the pitch of multiple strings at once.
The point is that he has composed pieces where he changes alternate tunings in the middle of the piece, without stopping.
Here he is explaining his system.
I just treat the five-string like a 6-string missing the high E. It's a lot easier than trying to figure out what notes to play on the B and makes for some super heavy sounding drop-D notes.
Tune it in EADGB and either play standard or drop the D. Unlike the person who took the actual heavier string and put it in the 5th string position, just tune it like a regular bass with one extra higher string.
One time, for fun, I strung one of my 5-strings EADGB. I just put the low B at the bottom of the strings instead of in it's usual position at the top. It was fun to mess with but not really practical. The reason I tried this was because I normally play 4-strings and wanted to have the feel of a 4-string with the option of playing a low B infrequently. Having the low B at the bottom kept it 'out of the way' in a sense.