Absolutely not. Active electronics are nice to have in a bass with any number of strings though, IMO.
Also, anecdotally, I've owned multiple active five-string basses, as well as multiple active four-strings that I've detuned to have a low C, and I've practically never used the active EQ on the bass to "shape" the low B or C string, with the exception that I occasionally give a very slight bass boost to one of my detuned four-stringers that tends to be a little less bass heavy than my other basses. For me if I use the onboard EQ on an active bass it is most often to give a little midrange bump or to partially reduce EQ differences between multiple basses I might swap between in a set. So for me there is no meaningful difference between the benefits of active on a five or four string to me.
Also, anecdotally, I've owned multiple active five-string basses, as well as multiple active four-strings that I've detuned to have a low C, and I've practically never used the active EQ on the bass to "shape" the low B or C string, with the exception that I occasionally give a very slight bass boost to one of my detuned four-stringers that tends to be a little less bass heavy than my other basses. For me if I use the onboard EQ on an active bass it is most often to give a little midrange bump or to partially reduce EQ differences between multiple basses I might swap between in a set. So for me there is no meaningful difference between the benefits of active on a five or four string to me.