The trajectory taken by the “Pirates of the Caribbean” franchise has been a peculiar one. First there was the surprisingly delightful “Curse of the Black Pearl” (2003), then the lumbering “Dead Man’s Chest” (2006), followed by the abominable “At World’s End” (2007). “On Stranger Tides” (2011) managed a marginal uptick, though its immediate predecessor had set the bar extremely low. Now “Dead Men Tell No Tales” is better still. It represents a very different kind of seagoing adventure for directors Joachim Ronning and Espen Sanberg, whose “Kon-Tiki” (2012) emphasized realism as much as this movie does fantasy.

They manage the transition decently enough, though the picture suffers from same sense of tiredness that marred all but the first entry. That’s particularly true of Johnny Depp, who returns as perpetually tipsy, fumbling Jack Sparrow. From the opening sequence—an overblown bank robbery which provides him with an entrance that would be pre-planned for applause if it were on Broadway and then lumbers on far too long—to the closing image of him sailing off again as captain of the Black Pearl, he seems to be merely going through the motions, doing ill-conceived slapstick dances and scrunching up his face to deliver lines that are meant to be drolly snarky but fall conspicuously flat. Jeff Nathanson’s script has its humorous moments, but virtually all of them are visual rather than verbal, and in Depp’s case even the visual ones are pretty anemic, save for a sequence involving a guillotine that shows some imagination but also runs on beyond its shelf life. (There is, however, a moment when Sparrow literally jumps over a shark—albeit a zombie one—that might be intended as a wry commentary on the whole enterprise.)

If Nathanson’s script offers Depp thin gruel, however, it has the virtue of nostalgically tying up loose ends from the earlier installments while adding some new characters, including one who explains Sparrow’s rise to piratical eminence. As a young seaman (where he is shown not via CGI trickery, but played by remarkable lookalike Anthony De La Torre), he outfoxed the notorious Spanish pirate-exterminator Captain Salazar (Javier Bardem), tricking him into guiding his ship into the so-called Triangle of Death, where Salazar and his crew were cursed into becoming ghouls doomed to sail forever in spectral form. Sparrow’s crew immediately elevated him to captaincy, where he quickly developed a penchant for items like rum.

“Tales” also offers a conclusion to the romance of Will Turner and Elizabeth Swann that was a major catalyst in the first three movies but dispensed with in the fourth. It does so through their son Henry, introduced as a boy (Lewis McGowen) who reconnects with his father, now the captain of the Flying Dutchman that reappears only every ten years, and then years later (now played by Brenton Thwaites) is searching for the only thing that can lift the curse on Will—the Trident of Poseidon, this installment’s MacGuffin. Happily he links up with Carina Smyth (Kaya Scodelario), an accused witch and self-proclaimed horologist (image how the pirates interpret that and you’ll have some idea of the script’s idea of wit). Those two will become a bickering couple who link up with Sparrow to track down the Trident.

Meanwhile Captain Barbossa (Geoffrey Rush), now a wealthy man in league with the British admiralty, gets word that Salazar and his ghostly crew are on the warpath trying to track down Sparrow, gobbling up England’s fleet in the process; and desiring to retrieve the miniaturized Black Pearl that Sparrow possesses, he agrees to lead Salazar to him, using the mystical compass that Sparrow has unwisely bartered for a bottle of booze. Of course, British ships are on the prowl as well. In short, everybody seems to be chasing everybody, their paths cross repeatedly, and the survivors all wind up at the uncharted island where the Trident is found and its power unleashed. Among other things, that will allow Henry to reunite his mother and father.

But that isn’t the only family matter “Tale” unveils, because Carina, an orphan, will discover the identity of her father as well. Even Sparrow—whose father we’d met in a previous installment played by Keith Richards, here gets a scene with his Uncle Jack, who’s played by Paul McCartney. Perhaps a musical family reunion is planned for the next installment, with Mick Jagger and Ringo Starr as additional brothers. In the meantime, the convoluted chase scenario allows for plenty of frantic CGI-heavy encounters at sea, one including Salazar’s undead crew literally walking on water. There’s even room for a weirdly gross interlude in which a captured Sparrow is almost forced to marry a grotesque island woman. (Bondage, incidentally, is a motif in the movie. Characters are repeatedly tied up—poor Thwaites so often that he might still be suffering from rope burn.)

The avalanche of special effects can’t help but have a regrettable impact on Paul Cameron’s 3D cinematography and Nigel Phelps’ production design, which are further hobbled by the messy editing of Roger Boston and Leigh Folsom Boyd in the action sequences. The visuals have a tendency to overwhelm the actors, too, especially Bardem, who must go through virtually the whole picture in wraith-like form; but everybody suffers in the big Trident finale, especially the person playing the character who—in a fashion that is quickly becoming a blockbuster cliché this summer (see “Guardians of the Galaxy, Vol. 2”)—chooses noble self-sacrifice over survival. Nonetheless Rush registers strongly again as Barbossa, while Thwaites and Scodelario make an attractive young couple and it’s pleasant to see Bloom and Keira Knightley together again, however fleetingly. All the cast are nicely frocked by costumer Penny Rose, and Geoff Zanelli’s score fills the bill, reusing some of the themes Klaus Badelt brought to “Black Pearl.”

“Dead Man Tell No Tales” is the most see-worthy entry in the “Pirates” franchise since the first installment, but still a comparatively leaky vessel, with Depp’s Sparrow in particular a shadow of his former self.