Depends on what kind of music you play, but.. no, you don't
have to get a 5-string. There's a thread here on TB about this very subject (Tried a Low B and Didn't Like it..); quite a spirited dabate, too. Lots of useful and enlightening info about BEAD and other alternative tunings. I posted on it, as I have my aluminum-necked Kramer 450B set up that way, with heavy Warwick Low B strings. Truly thunderous, but not really suitable for what I like to play. Interesting experiment, though.
I'm a lefty, too, by the way. My new Thunderbird should arrive at the Sam Ash here on Friday. Turns out the store in Canoga Park had one in stock -
MINE NOW! (Neener neener

) Will be interesting to see if it deposes my Rick 4001 as Most Favored Bass. Pix and request for number ASAP.