The addition of 5 extra notes on a five-string is only one reason to play fivers. I was an old beginner and, after lurking and absorbing what I could on Talkbass for a while, I decided to ignore the advice of those who suggested starting on a four and maybe working my way up to a five-string later. I'm very glad I did that. My reasons:
- Guitars have 6-strings and even GUITARISTS don't have a problem with six of them. I figured I was smart enough to be able to handle learning my way around five.

- You have more notes in a given position on the neck
- Can be easier to transpose key in real time
- I assumed I'd probably be playing covers far more often than originals, so I'd probably be transposing frequently to accomodate a singer. That turned out to be very true.
- Having more notes in one position can make sight reading easier (don't always have to read ahead as far in order to prepare for positional shifts, and you can often reduce the number of shifts you need to make).
- You have the additional notes if you want them (use them wisely!)
- Finally, you get to have some sadistic fun watching the confused looks on your guitar players faces when they try to follow your fretting hand before remembering that you play a fiver.
It's possible you'll get some stink eye from band mates. I've taken some crap from a couple of guitar players
*, partially in fun and partially not, and have also had a band leader ask if I had a "pro level bass" that I could use (I was playing a USA made G&L L-2500 at that audition). Not to defend them, but they were all older than me and had literally never played with a bass player who played anything but fours, so I guess they didn't know what to make of my basses. Not sure what they were worried about, but apparently they decided they liked my playing enough to not make anything of it. I suspect that if you fit musically, very few people you play with will actually have a problem with the instrument you play.
I say go for it you want a five string. Same goes for a four. Or a six. And if your teacher protests, I'd find a new teacher who is concerned with helping you become a better musician and is capable of helping you use your tool of choice to become that better musician.
* After playing my Stingray 5 and Jazz 5 the first several times I played with one band, a guitar player asked me if I had a "normal" bass. I asked what that was and he said something like "You know, like, a normal bass.". He wouldn't say it but I knew what he meant so I asked "You mean a Precision?". "Yeah, a Precision!!!". "Yeah, I have a Precision. I'll bring it next time". After I brought it a couple of times he was happy and told me how great that bass sounded compared to the others. So I asked him how it looked and he was confused. Then he realized he only looked at the name on the headstock and not at the number of tuners on it. It was a Fender Precision V.

He never complained after that, but he'd still kid me about them sometimes.
At least I think he was kidding ....