Of COURSE!
Fender was the first to offer 5-string basses.
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Although the above photo is not that of a vintage Fender, it adequately illustrates the Fender 5-stringer:
Four strings that are played, and a fifth decorative string on the "hang tag".
Unfortunately, most players do not realise the importance of the "hang" in a band situation, and remove the hang-tag (and thus its string).
If you've got the chops, but still can't seem to get into a band or stay in one for long — try putting the fifth string and hang-tag back.
Many players are rediscovering the importance of the "hang", and thus the rise in the popularity of five-string basses.
Some players have even managed to modify their basses to allow the playing of that fifth string, thus turning something that was once purely cosmetic into a functional and integral part of the bass.