Though retired, I spent 20+ years gigging, mostly as semi-professional, and several years as it with my only job.
When it comes to this evergreen '4-strings vs. (_____________ fill in how many string bass here)' question, I'll cut to the chase:
The only real question is not do I need one, but would a five (or whatever) help me make my best music. That's the only important question. Here's how, in the late 80's, I answered that question.
I started playing bass in the mid 70's. For about the first 10 years, I was never completely comfortable with a four string bass (and bear in mind, fives weren't available then). I came to electric bass from a classically trained keyboard background, and was never entirely comfortable with four strings in that I'd start a figure HERE and then have to shift up THERE to finish it. On keys, all the notes are in a straight line and don't repeat / overlap as on a stringed instrument.
So when fives began to be available from regular (not boutique) sources, I jumped in as now I could play across the strings in a more linear fashion that was more familiar. I found I could cover a lot of ground inside the space of a few frets. Also, there were a lot of keyboard bass parts in 80's music I could now easily duplicate on the bass.
And as others have pointed out, transposing, especially if you play with horns or singers who insist on 'other' keys for their songs, is a breeze. You just shift up or down a few frets, it's like shooting fish in a barrel.
I'd also advise that buying a completely different and foreign feeling bass (a five for occasional use for a long-time four string player) to pick up E-flat, D, D-flat, C, and open low B is a total aggravation and waste of money if you're not going to spend any real time with it. I'd also advise that a four-string bass and a five-string bass, to me, are two different instruments.
So for me, it simply suited my mind and outlook better, was far easier for me to play than a four, and I've played them exclusively since the late 80s (though on a whim I did buy a four-string Squier Jazz a few years ago). It gives me the best chance to do my best. Others can certainly have a different answer, but it simply suits me best in any way I can consider.