There are numerous reasons a sequel to The Fifth Element never got off the ground though, ranging from money concerns to Luc Besson's complicated past with the film's star Milla Jovovich. More than anything, it's probably got a lot to do with Besson's general aversion to directing sequels. Given how much time has passed since The Fifth Element first screamed into theaters, it's hard to believe he'd be hot to revisit those characters now.
Besson sort of did make a sequel to The Fifth Element in 2017, though it was very much "spiritual" in nature. That film was Besson's bizarro sci-fi epic Valerian and the City of a Thousand Planets, and while Valerian features no direct connections to the way-out-there wonders Besson conjured in The Fifth Element (Korben, Leelu and the gang are nowhere to be found), the worlds depicted in both films are similar.
If you're among those who bypassed Valerian and the City of a Thousand Planets when it was in theaters (and judging by its abysmal domestic box office returns, that's most of you), the film follows Dane DeHaan's titular Major and his wily partner Sergeant Laureline (Cara Delevingne) as they race to save space station Alpha, and ultimately the universe itself, from dastardly forces bent on destroying both.
There's a lot more going on in Valerian of course. Some might even argue there's a little too much going on in the film. That sort of judgment really does belong to each individual viewer though. Those viewers will not only recognize, but likely adore, the singular sort of creature-centric, serio-comic, world-building insanity that made The Fifth Element so much fun in every single frame of Valerian as well.