A five string bass is, unsurprisingly, a
bass guitar with 5 strings instead of the usual 4. They are usually
electric, although
acoustic and
upright models do exist.
The 5th string is usually a low B (2 octaves and a half step below middle C, IIRC), but variations have been spotted with a high C string (middle C exactly).
The low B string gives the bassist a greater ability to compete with keyboardists, since s/he can now play lower than was previously possible, into a realm that was once the province of the keyboardist's left hand. It also gives the bassist the ability to play songs in drop d without having to play higher on the neck (possibly ruining the feel of the song) or retuning/using a Hipshot key and having to deal with a new fretboard layout.
The high C string is useful for lead playing, or for emulating the sounds of a six string bass without the low end. This is occasionally favored by jazz players.
Five string upright basses are also exist, in the low-B variant; "every bassist worth his/her salt" supposedly owns one, or at least a double bass with a C extension (dropping the E string to C). No known high-C five-string variations of the double bass exist, although there are six-string variations, which are beyond the scope of this writeup.