Maybe....
If the pursuit of a 5 string is purely academic, as-in, you want a 5 sot that you can continue your bass learning, then I'm leaning toward advising you away from a 5.
Usually a 5 is for a particular need; some examples:
You play P&W or or gospel, jazz, etc. and have a need to access lower notes in order to complete your pallet of notes. Sometimes aesthetically the low notes on the B string are the deal and nothing else works. Take "Breathe" by The Brilliance. There just in NO substitute for that low D.
Breathe | The Brilliance - YouTube
Another reason to get a 5 is that you may be in a cover situation where you have a song like "Blood and Roses" Smithereens, or "Black Velvet" Alannah Myles and just don't want to have to have a second bass on standby tuned down half a step, or having to tune/re-tune real quick. Both are pretty do-able, but still a PITA.
So, convenience would be an argument for...
This next part is not an argument against, but rather, stuff that typically goes with the territory that you need to be aware of. Keep in mind, I like 5's and am right now between 5's right now. Am working on working with Warmoth on a 5 J Bass build, but very preliminary because:
Weight - I've had heavy basses before and am just over it. 9lbs. max is my rule, and the closer to 8 the better.
getting that in a budget-friendly 5 is challenging! I'm corresponding on the best strategy for a light-weight 5 and right now I think the plan is to do roasted wood all around; both body and neck. I hear-tell they have access to some lightweight swamp ash that could be further lightened by roasting...
The dreaded "floppy" B-String - I have been lucky as far as owing so far on the dreaded floppy/flabby B string thing. It happens when the geometry of the bass doesn't come together in such a way that the B can remain taught enough to sound solid and substantial. Strategies to combat it are string-thru the body bass. if you are talking about a full-size 34" bass, that can lead to buying special extra-long strings. 35" scale length is also a strategy to help the B string behave. I've owned both, and for me anyway, it's been fine.
Neck Width - If you have 5 strings you need a wider neck that you do if you have 4 strings. If you play with a technique that many players use where your thumb is in the middle of the back of the neck, a wider neck is going to be less of an adjustment. Some basses have tight string spacing, look at Ibanez and Schecter. If you have aspirations of "slapping", tight string spacing increases the difficulty. Personally I don't, so nothing lost there to me.
Tone Challenge - This isn't a real big one, but it's hard not to notice that most commercially produced 5 string basses have preamps. I think that part of this is because that's a consumer preference and if I was a bass mfg, I would produce what people want to buy. I also think that having a preamp built into the bass is something that people may consider to be a necessity so that they can easily dial in a usable tone that works in a variety of situations, making managing the B string, in deference the remaining 4 strings much easier. Either way, you could need to embrace the notion making sure you have full battery (or batteries, some take 2 9Vs) or spare batteries, and also make sure that you unplug your instrument lead to keep from unnecessarily running down your battery. Not a huge deal because batteries tend to last a long time, especially with more modern preamp designs. Still, more of a deal than a passive, no- battery bass. Do manufacturer's make passive 5's? of course. Am I going to build my Warmoth passive? definitely...
Switching from 5 to 4 and back - This could be a thing until you get used to it. I had trouble for a while. It's a thing, but it's a thing that doesn't last. At some point it will just mentally sink in that the fattest string on the bass neck isn't automatically going to be a B (or E for that matter).
Just some random thoughts from someone who's owned a few 5 string basses...
Hope it helps!!
Best,
WF